Question:
$\cosec 2\theta-\cot 2\theta=$
$\cosec 2\theta-\cot 2\theta=$
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Convert trigonometric expressions into sine and cosine for easy simplification.
Updated On: Mar 28, 2026
- $\tan\theta$
- $\sin 2\theta$
- $\cos\theta$
- $\tan 2\theta$
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The Correct Option is A
Solution and Explanation
Step 1: Using standard trigonometric identities.
\[ \cosec 2\theta-\cot 2\theta =\frac{1-\cos 2\theta}{\sin 2\theta} \]
Step 2: Simplifying using double angle formulas.
\[ 1-\cos 2\theta=2\sin^2\theta,\quad \sin 2\theta=2\sin\theta\cos\theta \]
Step 3: Final simplification.
\[ \frac{2\sin^2\theta}{2\sin\theta\cos\theta} =\frac{\sin\theta}{\cos\theta} =\tan\theta \]
Step 4: Conclusion.
\[ \cosec 2\theta-\cot 2\theta=\tan\theta \]
\[ \cosec 2\theta-\cot 2\theta =\frac{1-\cos 2\theta}{\sin 2\theta} \]
Step 2: Simplifying using double angle formulas.
\[ 1-\cos 2\theta=2\sin^2\theta,\quad \sin 2\theta=2\sin\theta\cos\theta \]
Step 3: Final simplification.
\[ \frac{2\sin^2\theta}{2\sin\theta\cos\theta} =\frac{\sin\theta}{\cos\theta} =\tan\theta \]
Step 4: Conclusion.
\[ \cosec 2\theta-\cot 2\theta=\tan\theta \]
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