Question

If cosθ = x, then ± √(1+x)/2 = _____.cosθ/2sinθ/2cos2θsin2θ

Answer 1

Answer:

cos(theta/2) = sqrt((1+x)/2)

Step-by-step explanation:

From the double angle formula

cos^2(t)-sin^2(t) = cos(2t)  ...................(1)

cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)

Add (1) and (2)

2cos^2(t) = 1+cos(2t)

cos^2(t) = (1+cos(2t))/2

cos(t) = sqrt((1+cos(2t))/2)

substitute t = theta/2

cos(theta/2) = sqrt((1+cos(theta))/2)

substitute cos(theta) = x

cos(theta/2) = sqrt((1+x)/2)