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P-2 Trigonometry — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Trigonometry1 Mark
Question
Prove that:
cot θ + tan θ = cosec θ sec θ

✓

Answer

Taking LHS, and putting $\cot \theta=\frac{\cos \theta}{\sin \theta}$ and $\tan \theta=\frac{\sin \theta}{\cos \theta}$
$\begin{array}{l}
=\cot \theta+\tan \theta \\
=\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta} \\
=\frac{\cos ^2 \theta+\sin ^2 \theta}{\sin \theta \cos \theta}\left[\text { As, } \sin ^2 \theta+\cos ^2 \theta=1\right] \\
=\frac{1}{\sin \theta \cos \theta} \\
=\operatorname{cosec} \theta \sec \theta \\
=\text { RHS }
\end{array}$
Proved!

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