Question

(1+cotA)2+(1-cotA)2=2cosec2A

Answer 1

Step-by-step explanation:

(1 + CotA)² + (1 - CotA)²

2 { (1)² + (CotA)² }

2 { 1 + Cot²A }

= 2Cosec²A

Answer 2

Your question:

Prove that (1+cotA)² + (1-cotA)² = 2cosec²A

Step-by-step explanation:

LHS = (1+cotA)² + (1-cotA)²

LHS = 1+cot²A+2cotA+1+cot²A-2cotA

LHS = 2(1+cot²A)

Now we apply the identity:1+cot²A=cosec²A

LHS = 2(cosec²A)

RHS = 2cosec²A

LHS = RHS

Hence proved

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