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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 4 · Set 3 · Q31
Prove that √(sec^2 θ+ cosec^2 θ)= tan θ+ cot θ. This section comprises Long Answer (LA) type questions of 5 marks each. 4 × 5=20
Prove that $\displaystyle \sqrt{\sec ^{2} \theta+\operatorname{cosec}^{2} \theta}=\tan \theta+\cot \theta$. This section comprises Long Answer (LA) type questions of $\displaystyle 5$ marks each. $\displaystyle 4 \times 5=20$
Marking-scheme solution
\[\begin{aligned}
\text { L.H.S } & =\sqrt{\sec ^{2} \theta+\operatorname{cosec}^{2} \theta} \\
& =\sqrt{1+\tan ^{2} \theta+1+\cot ^{2} \theta} \\
& =\sqrt{(\tan \theta+\cot \theta)^{2}} \\
& =\tan \theta+\cot \theta \\
& =\text { R.H.S }
\end{aligned}
\]
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