Question

If 11x is an acute angle and $\tan 11x=\cot 7x$, then what is the value of x?

• A. $5^{\circ }$
• B. $6^{\circ }$
• C. $7^{\circ }$
• D. $8^{\circ }$

Answer 1

The correct option is A $5^{\circ }$

$\tan 11x=\cot 7x$

$\Rightarrow \tan 11x=\tan (90°-7x)$

$\Rightarrow \tan 11x-\tan (90°-7x)=0$

$\Rightarrow \tan (11x-90°+7x)(1+\tan 11x.\tan (90°-7x))=0$

$\Rightarrow \tan (18x-90°)(1+\tan 11x.\tan (90°-7x))=0$

$\Rightarrow \tan (18x-90°)=0[\therefore 1+\tan 11x.\tan (90°-7x)\ne 0]$

$\Rightarrow \tan (10x-90°)=\tan 0°$

$\Rightarrow 18x-90°=0$

$\Rightarrow 18x=90°$

$\Rightarrow x=5°$

Hence, the answer is $5°.$