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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 2 · Set 3 · Q26
Prove that (cosec^2 θ- sec^2 θ)/(cosec^2 θ+ sec^2 θ)=3/4, if tan θ=1/(√ 7)
Prove that $\displaystyle \frac{\operatorname{cosec}^{2} \theta-\sec ^{2} \theta}{\operatorname{cosec}^{2} \theta+\sec ^{2} \theta}=\frac{3}{4}$, if $\displaystyle \tan \theta=\frac{1}{\sqrt{7}}$
Marking-scheme solution
\[\begin{aligned}
& \tan \theta=\frac{1}{\sqrt{7}} \\
& \Rightarrow \sec ^{2} \theta=\frac{8}{7} \text { and } \operatorname{cosec}^{2} \theta=8 \\
& \therefore \text { LHS }=\frac{8-\dfrac{8}{7}}{8+\dfrac{8}{7}}=\frac{3}{4}=\text { RHS }
\end{aligned}
\]
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