Question

cos square 1 + cos square 2 + ... cos square 90 + cos square 225 = ?

Answer 1

cos square 1 + cos square 2 + ... cos square 90 + cos square 225 = ?

Answer 2

Step-by-step explanation:

$\huge \boxed { \fcolorbox {green}{pink}{question:}}$

cos²1 + cos²2 + cos²3.............+ cos² 225

solution:

we know that:

cos²theta + sin² theta =1

also,

sin(90-theta)=costheta

thus, cos89 = sin1

so, we would cancel all the terms as 1 till cos 90° as 1........

cos90°=1

cos(180-theta )= -cos theta

thus, all the terms from cos 91 to cos 179 will get cancelled to 0

cos 180= 0

cos(180+theta)=-costheta...

thus, the answer will get simplified to 45+1 which is 46.....