Question

Prove that `2 sin^2  (3pi)/4 + 2 cos^2  pi/4 + 2 sec^2  pi/3` = 10

Answer 1

`sin  (3pi)/4 = sin 3 xx 45^circ = sin 135^circ`

= sin (180 - 45)

= sin 45° = `1/sqrt2`

`sec ((pi/3)) = 2`

`therefore 2 sin^2 ((3pi)/4) + 2 cos^2  pi/4 + 2 sec^2  pi/3`

`= 2 (sin  (3pi)/4)^2 + 2 (cos  pi/4)^2 + 2 (sec  pi/3)^2`

`= 2 (1/sqrt2)^2 + 2 (1/sqrt2)^2 + 2 (2)^2`

`= cancel(2)(1/cancel(2)) + cancel(2)(1/cancel(2)) + 2 (2)^2`

= 1 + 1 + 8 = 10

Hence proved.