RD Sharma Class 11 Solutions Chapter - Values of Trigonometric Functions at Sum of Difference | Mathematics (Maths) Class 11 - Commerce PDF Download

 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 that