Question

show that square root2+ √2 + √2+2 cos 4theta = 2cos theta/2
​

Answer 1

2+

2+2cos4θ

=2cosθ

squaring on both sides,

=> 2+

2+2cos4θ

=4cos

2

θ

=>

2+2cos4θ

=4cos

2

θ−2

=>

2+2cos4θ

=2(2cos

2

θ−1)

=>

2+2cos4θ

=2(cos2θ)

Again squaring,

=> 2+2cos4θ=4(cos

2

2θ)

=> 2cos4θ=4(cos

2

2θ)−2

=> 2cos4θ=2(2cos

2

2θ−1)

=> 2cos4θ=2(cos4θ)

=> LHS=RHS