Prove the following trignometric identities:

$(1 + c o t^{2} A) s i n^{2} A = 1$

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Solution

(1 + Cot² A) Sin² A = 1

Ans:

We know

$c o s e c^{2} θ - c o t^{2} θ = 1$

=>( $1 + c o t^{2} θ) s i n^{2} θ = c o s e c^{2} θ s i n^{2} θ$

$= (c o s e c θ s i n θ)^{2}$

= $(\frac{1}{s i n θ} s i n θ)^{2}$

= $(1)^{2}$ = 1

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