Question : If $\sin7x=\cos11x$, then the value of $\tan9x+\cot9x$ is:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
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Correct Answer: 2
Solution :
We know that $\sin(90° - \theta) = \cos\theta$
$\sin7x = \cos11x$
$⇒\sin7x = \sin (90° - 11x)$
$⇒7x = 90° - 11x$
$⇒18x = 90°$
$⇒x = 5°$
Substituting $x = 5°$ in $\tan9x+\cot9x$,
$\therefore\tan45° + \cot45°=1 + 1= 2$
Hence, the correct answer is $2$.
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