Question

Prove that $2sin^2 \frac{3π}{4}+2\,cos^2 \frac{π}{4}+2\,sec^2 \frac{π}{3}=10$

Answer 1

L.H.S. = $2sin^2 \frac{3π}{4}+2\,cos^2 \frac{π}{4}+2\,sec^2 \frac{π}{3}$

$=2\\{{sin{({\pi}\frac{\pi}{4})}}\\}^2+2(\frac{1}{√2})^2+2(2)^2$

$=2\\{sin{\pi}\frac{\pi}{4}\\}^2+2×\frac{1}{2}+8$

$=2(\frac{1}{√2})^2+1+8$

$1+1+8$

$=10$

$=R.H.S$