NCERT Class 11-Math's: Exemplar Chapter 3 Trigonometric Functions Part 10

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Question 6:

Prove that

Answer:

To prove:

As equation on RHS is a simplified expression, so we must opt Left side equation and simplify it further so that we can get

LHS = RHS.

And thus we will be able to prove it.

By seeing the expression we can think that the problem can be solved using transformation formula:

By transformation formula, we have:

But as LHS expression does not contain ‘2’ in its term. So we multiply and divide the expression by 2.

Applying transformation formula, we have –

Again, applying the transformation formula:

Hence:

Question 7:

Answer:

Given,

Squaring and adding equation 1 and 2, we get –

Using: , we get –

Question 8:

Find the value of tan ’.

Answer:

Question 9:

Answer:

As we know that-

From T-ratios of multiple angle, we know that

Hence: