if sin theta+cos theta=1..find sin theta,cos theta

sinθ + cosθ = 1

sinθ = 1 - cosθ

Now using the identity,

sin²θ + cos²θ = 1

Put sinθ = 1 - cosθ

(1 - cosθ)² + cos²θ = 1

1 - 2cosθ + 2cos²θ = 1

cos²θ - cosθ = 0

cosθ ( cosθ - 1) = 0

cosθ = 0 or 1

Hence sinθ = 0 or 1

If we need sinθcosθ,

it's ZERO.

We can verify,

sinθ + cosθ = 1

Squaring both sides,

sin²θ + 2sinθcosθ + cos²θ = 1

sinθcosθ= 0

 

Regards,

Team,

TopperLearning.