If sin θ + cos θ = x; what is the value of sinθ.cosθ ?
Answer & explanation
Correct answer: option 2
sin θ + cos θ = x
⇒sin θ - cos θ = \(\frac{1}{x}\)
4sinθ.cosθ = (sinθ + cosθ)2 - (sinθ - cosθ)2
⇒ 4sinθ.cosθ = x2 - \(\frac{1}{x^2}\)
⇒ sinθ.cosθ = \(\frac{1}{4}\)(x2 - \(\frac{1}{x^2}\))