Question #7ec3c

2 Answers
Feb 13, 2018

π3;5π3

Explanation:

2cos2(t2)3cost=0
Using identity (1+cos2a=2cos2a), replace in the equation
2cos2(t2) by (1+cost).
We get:
1 + cos t - 3cos t = 0
cost=12
Trig Table and unit circle give 2 solutions:
t=±π3, or
t=π3, and t=5π3 (co-terminal to (π3))

Feb 13, 2018

Give a look here...

Reference proof:-

cosθ=cos2(θ2)sin2(θ2)
cosθ=cos2(θ2)1+cos2(θ2)
cosθ=2cos2(θ2)1

Explanation:

2cos2(θ2)3cosθ=0
(cosθ+1)3cosθ=0
2cosθ=1
cosθ=12
cosθ=cos(π3)
θ=2nπ±(π3) [nI]

for n=0θ=π3
for n=1θ=5π3

Hope it helps...
Thnx...