Question

If $\sin x+\cos x+\tan x+\cot x+\sec x+cosecx=7$ and $\sin 2x=a-b\sqrt{7}$, then-

• A. $a=8$
• B. $b=22$
• C. $a=22$
• D. $b=8$

Answer 1

Answer: (C), (D)

The correct options are
C $a=22$
D $b=8$

$(\sin x+\cos x)+\left(\frac{1}{\sin x\cos x}\right)+\left(\frac{\sin x+\cos x}{\sin x\cos x}\right)=7$
$\Rightarrow (\sin x+\cos x)(1+\frac{1}{\sin x\cos x})=7-\frac{2}{\sin 2x}$
Squaring both sides $\Rightarrow {\sin }^{2}2x-44{\sin }^{2}2x+36\sin 2x=0$
$\Rightarrow {\sin }^{2}2x-44\sin 2x+36=0(\sin 2x\ne 0)$
$\Rightarrow \sin 2x=22-8\sqrt{7}$.
Option C and D