Question

for what value of tita is sin tita =cos 2 tita​

Answer 1

Step-by-step explanation:

Well, cos(2θ)=cos²(θ)-sin²(θ). (Identity)

Now, sin(θ)=cos²(θ)-sin²(θ)

Use, cos²(θ)=1-sin²(θ)

=> sin(θ)= 1-sin²(θ)-sin²(θ)

=> sin(θ)= 1-2sin²(θ)

Substitute sin(θ)=x.

=> x=1-2x²

=>2x²+x-1=0

=>2x²+2x-x-1=0

=>2x(x+1)-1(x+1)=0

=>(x+1)(2x-1)=0

=>x=-1 or x=1/2

sin(θ)=-1 or sin(θ)=1/2

On checking θ=270° or 3π/2(from sin(θ)=-1) with original equation, it makes no sense.

For, θ=30° or π/3, we get things right.

You can generalise the result for other quadrants.