Question

If $sinx+cosx+tanx+cotx+secx+cosecx=7$ and $sin2x=a-b\sqrt{7}$ , then $a-b+14$ is divisible by

• A. $5$
• B. $3$
• C. $0$
• D. $7$

Answer 1

The correct option is D $7$

$sinx+cosx+\frac{1}{sinxcosx}+\frac{sinx+cosx}{sinxcosx}=7$

$(sinx+cosx)[1+\frac{2}{sin2x}]=7-\frac{2}{sin2x}$

$square(1+sin2x){[1+\frac{2}{sin2x}]}^2=49+\frac{4}{si{n}^{2}2x}-\frac{28}{sin2x}$

$sin2x=t$ solve it $t^2-44t+36=0$

$sin2x=22-8\sqrt{7}$

$a=22,b=8$