Question

(1)/(2+cot^(2)(-theta))=(1)/(2 csc^(2)(-theta)-cot^(2)(-theta))​

Answer 1

we have to prove that, 1/(2 + cot²θ) = 1/(2cosec²θ - cot²θ)

proof : LHS = 1/(2 + cot²θ)

= 1/(1 + 1 + cot²θ)

= 1/{1 + (1 + cot²θ)}

we know, 1 + cot²θ = cosec²θ

= 1/{1 + cosec²θ}

using 1 = cosec²θ - cot²θ

= 1/{cosec²θ - cot²θ + cosec²θ}

= 1/{2 cosec²θ - cot²θ}

= 1/(2cosec²θ - cot²θ) = RHS

hence proved

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Answer 2

Step-by-step explanation:

hope this helps you!!!!!!