Question

The value of cos²(π/8)+cos²(3π/8)+cos²(5π/8)+cos²(7π/8) is *​

Answer 1

cos^2(π/8) + cos^2(3π/8) + cos^2(5π/8) + cos^2(7π/8)  

= cos^2(π/8) + cos^2(π/2 - π/8) + cos^2(5π/8) + cos^2(π/2 - (-3π/8))  

= cos^2(π/8) + sin^2(π/8) + cos^2(5π/8) + sin^2(-3π/8)  

= cos^2(π/8) + sin^2(π/8) + cos^2(5π/8) + sin^2(5π/8) -----> sin(-3π/8) = -sin(5π/8) but after squaring it becomes positive anyway  

= 1 + 1  

= 2