Question

cosec square thita - sec square thita=cot square thita -tan square thita

Answer 1

$\textbf{To prove:}$

$cosec^2\theta-sec^2\theta=cot^2\theta-tan^2\theta$

$\textbf{Solution:}$

$\text{Consider,}$

$cosec^2\theta-sec^2\theta$

$\text{Using}$

$\boxed{\bf\,cosec^2A=1+cot^2A}$

$\boxed{\bf\,sec^2A=1+tan^2A}$

$=(1+cot^2\theta)-(1+tan^2\theta)$

$=1+cot^2\theta-1-tan^2\theta$

$=cot^2\theta-tan^2\theta$

$\therefore\bf\,cosec^2\theta-sec^2\theta=cot^2\theta-tan^2\theta$

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