Question

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Q.no. 9

Answer 1

hiiii mate ...good morning..

here is ur solution..

I hope it's help..

Answer 2

(Instead of θ, I use A)

Answer:

Step-by-step explanation:

Given :

To prove : $\frac{1}{sinA + CosA} + \frac{1}{sinA - CosA} = \frac{2SinA}{1-2Cos^2A}$

Proof :

We know that Sin²A + Cos²A = 1,

⇒ Sin²A = 1 - Cos²A ...(i)

LHS =  $\frac{1}{sinA + CosA} + \frac{1}{sinA - CosA}$

⇒ $\frac{1(SinA-CosA) + 1(SinA + CosA}{(SinA + CosA)(SinA - CosA)}$

⇒ $\frac{SinA + CosA + SinA - CosA}{Sin^2A - Cos^2A}$

⇒ $\frac{2SinA}{Sin^2A - Cos^2A}$

⇒ $\frac{2SinA}{(1 - Cos^2A) - Cos^2A}$  ( by (i) )

⇒ $\frac{2SinA}{1 - 2Cos^2A}$ = RHS