**Question 1.Find the values of:**

**Question 2.**

**Question 3.**

**v. tan x + cot x = 2 cosec 2xSolution:**

L.H.S. = tan x + cot x

Solution:

Solution:

= 2 cos x

= R.H.S.

[Note : The question has been modified.]

**viii. 16 sin θ cos θ cos 2θ cos 4θ cos 8θ = sin 16θSolution:**

L.H.S. = 16 sin θ cos θ cos 2θ cos 4θ cos 8θ

= 8(2sinθ cosθ) cos2θ cos 4θ cos 8θ

= 8sin 2θ cos 2θ cos 4θ cos 8θ

= 4(2sin 2θ cos 2θ) cos 4θ cos 8θ

= 4sin 4θ cos 4θ cos 8θ

= 2(2sin 4θ cos 4θ) cos 8θ

= 2sin 8θ cos 8θ

= sin 16θ

= R.H.S.

**ix. \( = 2 cot 2xSolution:**

**x. [latex]\frac{\cos x}{1+\sin x}=\frac{\cot \left(\frac{x}{2}\right)-1}{\cot \left(\frac{x}{2}\right)+1}\)Solution:**

Solution:

Solution:

Solution:

Solution:

**xvii. 2 cosec 2x + cosec x = sec cot x/2Solution:**

Solution: