Question

$\cosec 2\theta-\cot 2\theta=$

• A. $\tan\theta$
• B. $\sin 2\theta$
• C. $\cos\theta$
• D. $\tan 2\theta$

Hint:

Convert trigonometric expressions into sine and cosine for easy simplification.

Answer 1

The Correct Option is A

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.
\[ \cosec 2\theta-\cot 2\theta=\tan\theta \]