Question

solve this trigonometry question

Answer 1

sin^2 x + cos^2 x = 1
Square both sides
=> sin^4 x + cos^4 x + 2 sin^2 x cos^2 x = 1
=> 1/2 +2 sin^2 x cos^2 x = 1
=> 2 sin^2 x cos^2 x = 1/2
=> sin^2 x cos^2 x = 1/4
=> sin x cos x = 1/2

Answer 2

Solution:

★ we know that sin⁴θ + cos⁴θ = 1 - 2 sin²θ cos²θ

Given, sin⁴θ + cos⁴θ = ½

→ 1 - 2 sin²θ cos²θ = ½

½ = 2 sin²θ cos²θ → (sinθ cosθ)²

→ sinθ cosθ = ± ½

Hope it's help ful to you