Question

Use a trigonometric identity to find exactly all solutions: cos 20 = sin , 0<o<21. Enter the exact answers in increasing order. O= Edit 6 31 Edit 2 II 5a 6 Edit

Answer 1

Solution :- Given that

cos2θ=sinθ where θ lie in the interval

[0,2π).

Now,

cos2θ=sinθ

1-2sin^2(θ)=sinθ {where cos2θ=1-2sin^2(θ)}

Multiplication both side by negative sign

-1+2sin^2(θ)=-sinθ

2sin^2(θ)+sinθ-1=0

2sin^2(θ)+2sinθ-sinθ-1=0

2sinθ(sinθ+1)-1(sinθ+1)=0

(2sinθ-1).(sinθ+1)=0

If 2sinθ-1=0

2sinθ=1

sinθ=1/2

θ=π/6 =30° OR θ =5π/6=150°

If sinθ+1=0

sinθ=-1

θ=3π/2=270°

Hence the Exact value of θ in increasing

order is 3π/2

Hence the correct answer is 3π/2