NCERT Class 11 Math's Exemplar Chapter 3 Trigonometric Functions Part 5

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Question 10:

If then find the value of

Answer:

Note that

If we put

Then

So that

Hence,

Question 11:

If α and are the solutions of the equation , then show that

Answer:

Given that he identities,

We have,

Or

Above equation is quadratic in tan and hence tan and tan are the roots of this equation (Why?). Therefore, and

Using the identity

We have,

Again, using another identity

We have

Alternatively, given that

nce α and β are the roots of the equation , so

Therefore,

Question 12:

Show that

Answer:

(Why?)