Evaluate the trigonometric relation If

Question

 sin(Π cosΘ) = cos ( ΠsinΘ)

then evaluate |sin 2Θ|

Answer 1

Sine is equal to cosine if their angles add up to π/2.

 

πcosθ + πsinθ = π/2

 

2ncosθ + 2nsinθ = π

 

2π(cosθ + sinθ) = π

 

cosθ + sinθ = 1/2

 

 

√(1 - sin²θ) + sinθ - 1/2 = 0

  

 

Solve for sinθ from the bold equation.  Then once you found sinθ, use the Pythagorean identity to find cosθ.  Finally, use the double-angle identity to find  sin2θ.