Question

if sinθ-cosθ=1, find the value of cosθ+sinθ

Answer 1

Let theta equal to a for convenience...

Thus, (sina-cosa)^2=sin^2a+cos^2a - 2sinacosa

=1-2sinacosa............1

(sina+cosa)^2=sin^2a+cos^a+ 2sinacosa........2

Add 1 and 2 ,

you get,

(sina-cosa)^2+(sina+cosa)^2=2

We know that, sina-cosa=1,

Therefore, (sina-cosa)^2=1^2=1

Thus, sina+cosa=2-1

=root1

=1

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