Commerce Exam  >  Commerce Notes  >  Mathematics (Maths) Class 11  >  NCERT Solutions: Exercise Miscellaneous - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Question 1: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

 

ANSWER : L.H.S.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

= 0 = R.H.S

 

Question 2: Prove that: (sin 3+ sin x) sin +(cos 3– cos x) cos = 0

 

ANSWER : L.H.S.

= (sin 3x + sin x) sin x + (cos 3– cos x) cos x

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

= RH.S.

 

Question 3: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

ANSWER : L.H.S. =  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

                                   NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions


Question 4: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

ANSWER : L.H.S. =  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

                                   NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

 

Question 5: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

 ANSWER : It is known that NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

∴L.H.S. =  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

              NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

 

Question 6: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

ANSWER : It is known that

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

L.H.S. =  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

           NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

           = tan 6x

           = R.H.S.

 

Question 7: Prove that:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

ANSWER : L.H.S. =  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

                                   NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

 

Question 8:  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions , x in quadrant II

ANSWER : Here, x is in quadrant II.

i.e., NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Therefore,  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  are all positive.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

As x is in quadrant II, cosx is negative.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Thus, the respective values of  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions are NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

 

Question 9: Find NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  for  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions , x in quadrant III

 

ANSWER : Here, x is in quadrant III.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Therefore,  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  and  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  are negative, whereas NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions is positive.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Now,  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Thus, the respective values of  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions are NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

.

Question 10: Find NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  for  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions , x in quadrant II

 

ANSWER : Here, x is in quadrant II.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Therefore, NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions , and  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  are all positive.

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions [cosx is negative in quadrant II]

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

Thus, the respective values of NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions  are  NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions .

NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

The document NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions is a part of the Commerce Course Mathematics (Maths) Class 11.
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FAQs on NCERT Solutions Class 11 Maths Chapter 3 - Trigonometric Functions

1. What are trigonometric functions?
Ans. Trigonometric functions are mathematical functions that relate the angles of a triangle to the ratios of its sides. These functions include sine, cosine, tangent, cosecant, secant, and cotangent.
2. How are trigonometric functions used in real-life applications?
Ans. Trigonometric functions have various real-life applications, such as in navigation, engineering, physics, and astronomy. They are used to calculate distances, angles, heights, and trajectories in these fields.
3. What is the unit circle and how is it related to trigonometric functions?
Ans. The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. It is used to define trigonometric functions by relating them to the coordinates of points on the circle. The x-coordinate represents the cosine function, and the y-coordinate represents the sine function.
4. How can I find the values of trigonometric functions for specific angles?
Ans. Trigonometric functions can be evaluated using special triangles, the unit circle, or trigonometric identities. These methods allow you to find the values of trigonometric functions for angles such as 0°, 30°, 45°, 60°, and 90°, as well as their multiples.
5. Are there any important identities or formulas related to trigonometric functions?
Ans. Yes, there are several important identities and formulas related to trigonometric functions. These include Pythagorean identities, sum and difference formulas, double angle formulas, half-angle formulas, and reciprocal identities. These identities are useful in simplifying trigonometric expressions and solving trigonometric equations.
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