Commerce Exam > Commerce Notes > Mathematics (Maths) Class 11 > RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values
RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values
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Page 1 7. Values of Trigonometric Functions at Sum of Difference of Angles Exercise 7.1 1. Question If sinA = 4/5 And cosB = 5/13, where 0 <A, B < p/2, find the values of the following: (i) sin(A +B) (ii) cos(A +B) (iii) sin(A –B) (iv) cos(A -B) Answer Given sinA = 4/5 And cosB = 5/13 We know that where 0 <A,B < p/2 Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB (iii) Sin(A –B) Page 2 7. Values of Trigonometric Functions at Sum of Difference of Angles Exercise 7.1 1. Question If sinA = 4/5 And cosB = 5/13, where 0 <A, B < p/2, find the values of the following: (i) sin(A +B) (ii) cos(A +B) (iii) sin(A –B) (iv) cos(A -B) Answer Given sinA = 4/5 And cosB = 5/13 We know that where 0 <A,B < p/2 Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB (iii) Sin(A –B) We know that sin(A -B) = sinA cosB - cosA sinB (iv) Cos(A –B) We know that cos(A -B) = cosA cosB + sinA sinB 2 A. Question If SinA = 12/13 And sinB = 4/5, where p/2<A < p And 0 <B < p/2, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given sinA = 12/13 And sinB = 4/5 where p/2 <A < p And 0 <B < p/2 We know that (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB Page 3 7. Values of Trigonometric Functions at Sum of Difference of Angles Exercise 7.1 1. Question If sinA = 4/5 And cosB = 5/13, where 0 <A, B < p/2, find the values of the following: (i) sin(A +B) (ii) cos(A +B) (iii) sin(A –B) (iv) cos(A -B) Answer Given sinA = 4/5 And cosB = 5/13 We know that where 0 <A,B < p/2 Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB (iii) Sin(A –B) We know that sin(A -B) = sinA cosB - cosA sinB (iv) Cos(A –B) We know that cos(A -B) = cosA cosB + sinA sinB 2 A. Question If SinA = 12/13 And sinB = 4/5, where p/2<A < p And 0 <B < p/2, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given sinA = 12/13 And sinB = 4/5 where p/2 <A < p And 0 <B < p/2 We know that (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB 2 B. Question If sinA = 3/5, cosB = –12/13, where A And B Both lie in second quadrant, find the value of sin(A +B). Answer Given sinA = 3/5 And cosB = -12/13 A And B lie in the second quadrant. So sine function is positive And cosine function is negative. We know that Now consider sin(A +B), ? sin(A +B) 3. Question If cosA = – 24/25 And cosB = 3/5, where p <A < 3p/2 And 3p/2 <B < 2p, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given cosA = -24/25 And cosB = 3/5 where p <A < 3p/2 And 3p/2 <B < 2p A is in third quadrant And B is in fourth quadrant. Here, sine function is negative. We know that Page 4 7. Values of Trigonometric Functions at Sum of Difference of Angles Exercise 7.1 1. Question If sinA = 4/5 And cosB = 5/13, where 0 <A, B < p/2, find the values of the following: (i) sin(A +B) (ii) cos(A +B) (iii) sin(A –B) (iv) cos(A -B) Answer Given sinA = 4/5 And cosB = 5/13 We know that where 0 <A,B < p/2 Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB (iii) Sin(A –B) We know that sin(A -B) = sinA cosB - cosA sinB (iv) Cos(A –B) We know that cos(A -B) = cosA cosB + sinA sinB 2 A. Question If SinA = 12/13 And sinB = 4/5, where p/2<A < p And 0 <B < p/2, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given sinA = 12/13 And sinB = 4/5 where p/2 <A < p And 0 <B < p/2 We know that (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB 2 B. Question If sinA = 3/5, cosB = –12/13, where A And B Both lie in second quadrant, find the value of sin(A +B). Answer Given sinA = 3/5 And cosB = -12/13 A And B lie in the second quadrant. So sine function is positive And cosine function is negative. We know that Now consider sin(A +B), ? sin(A +B) 3. Question If cosA = – 24/25 And cosB = 3/5, where p <A < 3p/2 And 3p/2 <B < 2p, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given cosA = -24/25 And cosB = 3/5 where p <A < 3p/2 And 3p/2 <B < 2p A is in third quadrant And B is in fourth quadrant. Here, sine function is negative. We know that Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB 4. Question If tanA = 3/4, cosB = 9/41, where p<A < 3p/2 And 0 <B < p/2, find tan(A +B). Answer Given tanA = 3/4 And cosB = 9/41 where p <A < 3p/2 And 0 <B < p/2 A is in third quadrant And B is in first quadrant. Tan function And sine function are positive. We know that Page 5 7. Values of Trigonometric Functions at Sum of Difference of Angles Exercise 7.1 1. Question If sinA = 4/5 And cosB = 5/13, where 0 <A, B < p/2, find the values of the following: (i) sin(A +B) (ii) cos(A +B) (iii) sin(A –B) (iv) cos(A -B) Answer Given sinA = 4/5 And cosB = 5/13 We know that where 0 <A,B < p/2 Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB (iii) Sin(A –B) We know that sin(A -B) = sinA cosB - cosA sinB (iv) Cos(A –B) We know that cos(A -B) = cosA cosB + sinA sinB 2 A. Question If SinA = 12/13 And sinB = 4/5, where p/2<A < p And 0 <B < p/2, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given sinA = 12/13 And sinB = 4/5 where p/2 <A < p And 0 <B < p/2 We know that (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB 2 B. Question If sinA = 3/5, cosB = –12/13, where A And B Both lie in second quadrant, find the value of sin(A +B). Answer Given sinA = 3/5 And cosB = -12/13 A And B lie in the second quadrant. So sine function is positive And cosine function is negative. We know that Now consider sin(A +B), ? sin(A +B) 3. Question If cosA = – 24/25 And cosB = 3/5, where p <A < 3p/2 And 3p/2 <B < 2p, find the following: (i) sin(A +B) (ii) cos(A +B) Answer Given cosA = -24/25 And cosB = 3/5 where p <A < 3p/2 And 3p/2 <B < 2p A is in third quadrant And B is in fourth quadrant. Here, sine function is negative. We know that Then, (i) Sin(A +B) We know that sin(A +B) = sinA cosB + cosA sinB (ii) Cos(A +B) We know that cos(A +B) = cosA cosB - sinA sinB 4. Question If tanA = 3/4, cosB = 9/41, where p<A < 3p/2 And 0 <B < p/2, find tan(A +B). Answer Given tanA = 3/4 And cosB = 9/41 where p <A < 3p/2 And 0 <B < p/2 A is in third quadrant And B is in first quadrant. Tan function And sine function are positive. We know that We know that We know that 5. Question If sinA = 1/2, cosB = 12/13, where p/2<A < p And 3p/2 <B < 2p, find tan(A -B). Answer Given sinA = 1/2 And cosB = 12/13 where p/2 <A < p And 3p/2 <B < 2p A is in second quadrant And B is in fourth quadrant. In the second quadrant, the sine function is positive And cosine And tan functions negative. In the fourth quadrant, sine And tan functions are negative, And cosine function are positive. We know thatRead More
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Document Description: RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values for Commerce 2026 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values have been prepared according to the Commerce exam syllabus. Information about RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values covers topics like and RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values Example, for Commerce 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Values.
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