Question
Write the value of $\text{cosec}^2(90^\circ-\theta)-\tan^2\theta$.
✓
Answer
$\text{cosec}^2(90^\circ-\theta)\tan^2\theta$
$=\sec^2\theta-\tan^2\theta=1$
$\begin{cases}\because \text{cosec }(90^\circ-\theta)=\sec\theta \\ \text{and }\sec^3\theta-\tan^3\theta=1 \end{cases}$
$=\sec^2\theta-\tan^2\theta=1$
$\begin{cases}\because \text{cosec }(90^\circ-\theta)=\sec\theta \\ \text{and }\sec^3\theta-\tan^3\theta=1 \end{cases}$
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