Question

Prove that (1+cot teta)² +(1- cot teta)² = 2 cosec²teta
please answer in step by step process and correctly
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Answer 1

Answer:

We know that (a+b)²+(a-b)²=2(a²+b²)

so,(1+cot theta)²+(1-cot theta)²=2(1+cot²theta)

we know that 1+cot² theta=cosec²theta

so the answer is 2cosec²theta

hence proved

Answer 2

Step-by-step explanation:

(1+cot theta)²+(1-cot theta)²=2cosec² theta

L.H.S= 1²+cot² theta+2×1× cot theta+1²+cot² theta -2×1×cot theta

=cosec² theta +2cot theta+cosec² theta -2cot theta

=2cosec²theta R.H.S