Question

Prove that

(i) cos(π/3 + x) = 1/2(cosx - √3 sinx)

(ii) sin(π/4 + x) + sin(π/4 - x) = √2 cosx

(iii) 1/√2 cos(π/4 + x) = 1/2(cosx - sinx)

(iv) cosx + cos(2π/3 + x) + cos(2π/3 - x) = 0

Answer 1

(i) \(cos(\frac{\pi}{3}+x)=cos\frac{\pi}{3}.cosx-sin\frac{\pi}{3}.sinx\)

(ii) \(sin(\frac{\pi}{4}+x)+sin(\frac{\pi}{4}-x)\)

= cosx - cosx \(\Rightarrow\) 0