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Evaluate ^{2}(^{2}+1)=^{2}-1

Question

Evaluate
$sin^{2} θ (tan^{2} θ + 1) = sec^{2} θ - 1$

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Evaluate

sin^{2} θ (tan^{2} θ + 1) = sec^{2} θ - 1

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Text solutionVerified

s i n^{2} θ (t a n^{2} θ + 1) = se c^{2} θ - 1

\Rightarrow

s i n^{2} θ . se c^{2} θ = se c^{2} θ - 1

\Rightarrow

s i n^{2} θ . se c^{2} θ - se c^{2} θ = - 1

\Rightarrow

se c^{2} θ (s i n^{2} θ - 1) = - 1

LHS,

\Rightarrow

se c^{2} θ (- co s^{2} θ)

\Rightarrow

- 1

= RHS

Hence proved

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