Question

.Prove that. sec2 0 + cosec2 0 = sec2 0.cosec2 0.​

Answer 1

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$Prove\ that: \\ sec^2 \theta + cosec^2 \theta = sec^2 \theta . cosec^2 \theta$

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$\boxed{\red{\bold{Solving\ LHS:}}}$

$\purple{\implies sec^2 \theta + cosec^2 \theta}$

$\purple{\implies}\displaystyle \frac{1}{cos^2 \theta} + \frac{1}{sin^2 \theta}$

$\blue{\left( \because sec^2 \theta = \displaystyle{\frac{1}{cos^2 \theta}} \ and\ cosec^2 \theta = \frac{1}{sin^2 \theta}\right)}$

${\purple{\implies}}\displaystyle \frac{sin^2 \theta + cos^2 \theta}{sin^2 \theta . cos^2 \theta}$

$\purple{\implies}\displaystyle \frac{1}{sin^2 \theta . cos^2 \theta}$

$\blue{(\because cos^2 \theta + sin^2 \theta = 1)}$

$\green{\boxed{\implies{\boxed{cosec^2 \theta . sec^2 \theta = RHS}}}}$

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