NCERT Class 11 Math՚S Exemplar Chapter 3 Trigonometric Functions Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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?)