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

Asked by nmishra320 | 20th Jan, 2010, 12:12: PM

Expert Answer:

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.

Answered by  | 20th Jan, 2010, 01:01: PM

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