Thread: trigonometry

If , then the expression [√2+√2(1+cos4θ)]is simplified to _________ .
1) 2cosθ
2) 2sinθ
3) -2cosθ
4) -2sinθ
(its a single choice question)

Originally Posted by gkpandey

If , then the expression [√2+√2(1+cos4θ)]is simplified to _________ .
1) 2cosθ
2) 2sinθ
3) -2cosθ
4) -2sinθ
(its a single choice question)

[√2+√2(1+cos4θ)]
[√2+√2 . 2cos^2 2θ] [1+cos4θ=2cos^2 2θ , half the angle formula]
√2{1+2cos^2 2θ]
v2 {1+2(2cos^2 θ-1)
v2{2cos^2 θ -1}

Originally Posted by gkpandey

If , then the expression [√2+√2(1+cos4θ)]is simplified to _________ .
1) 2cosθ
2) 2sinθ
3) -2cosθ
4) -2sinθ
(its a single choice question)

i think your question is

√[2+√{2*(1+cos 4θ)}] = ?

use identity
1+cos2θ = 2 cos^2 θ
and cos4θ =cos2(2θ )

solve the sum to get answer
1) 2cosθ