Question

Prove that :- {(1+cosA)^2 +(1-cosA) ^2} ÷ {sin^2A} = 2 (1+2cot^2A)​

Answer 1

I think this question is wroung the RHS must be like 2(1+cosec^2A)

Answer 2

Explanation:

(a + b)² + (a - b)² = 2(a² + b²)

a = 1 ; b = Cos A

(1 + Cos A)² + (1 - Cos A)² = 2(1² + Cos² A)

= 2(1 +Cos² A) ----------(I)

LHS = { (1 + Cos A)² + (1 - Cos A)²} ÷ { Sin² A}

= { 2( 1 + Cos² A )} ÷ Sin² A {From (I)}

= { 2 (Sin² A + Cos² A + Cos² A) } ÷ { Sin² A} {Here, Sin² A + Cos² A = 1 }

= 2 (Sin² A + 2Cos² A) } ÷ { Sin² A}

`= 2 ( (Sin^(2) A)/(Sin^2 A) + (2Cos^(2) A)/(Sin^(2) A))`

= 2( 1 + 2 Cot² A) =RHS