NCERT Class 11-Math's: Exemplar Chapter 3 Trigonometric Functions Part 6

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Question 13:

If angle is divided into two parts such that the tangent of one part is times the tangent of other, and φ is their difference, then show that

Answer:

Or

Applying componendo and dividendo, we have

Or

Given that . Therefore,

Question 14:

Solve

Answer:

Divide the given equation by 2 to get

Thus, the solution are given by, i.e.,

Hence, the solution are

Objective Type Questions

Choose the Correct Answer from the Given Four Options Against Each of the Examples 15 to 19

Question 15:

If tan is (A)

(B)

(C)

(D) None of these

Answer:

Correct choice is B. Since is negative, θ lies either in second quadrant or in fourth quadrant. Thus if lies in the second quadrant or , if lies in the fourth quadrant.

Question 16:

If and are the roots of the equation, then a, b and c satisfy the relation.

(A)

(B)

(C)

(D)

Answer:

The correct choice is (B).

Given that and are the roots of the equation = (Why?)

Using the identity , we have

Question 17:

The greatest value of is

(A)

(B)

(C)

(D)

Answer:

(D) is the correct choice, since