MHT CET · Maths · Trigonometric Ratios & Identities
\(\operatorname{cosec} 2 \theta-\cot 2 \theta=\)
- A \(\tan \theta\)
- B \(\sin 2 \theta\)
- C \(\cos \theta\)
- D \(\tan 2 \theta\)
Answer & Solution
Correct Answer
(A) \(\tan \theta\)
Step-by-step Solution
Detailed explanation
(D)
\(\begin{aligned}
\operatorname{cosec} 2 \theta-\cot 2 \theta &=\frac{1}{\sin 2 \theta}-\frac{\cos 2 \theta}{\sin 2 \theta} \\
&=\frac{1-\cos 2 \theta}{\sin 2 \theta}=\frac{2 \sin ^{2} \theta}{2 \sin \theta \cos \theta}=\tan \theta
\end{aligned}\)
\(\begin{aligned}
\operatorname{cosec} 2 \theta-\cot 2 \theta &=\frac{1}{\sin 2 \theta}-\frac{\cos 2 \theta}{\sin 2 \theta} \\
&=\frac{1-\cos 2 \theta}{\sin 2 \theta}=\frac{2 \sin ^{2} \theta}{2 \sin \theta \cos \theta}=\tan \theta
\end{aligned}\)
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