Question

sin theta+ cos theta= 1 then prove that sin theta -cos theta =+-1

Answer 1

(sin theta + cos theta)^2 = 1^2

sin^2 theta + cos^2 theta + 2 sin theta * cos theta = 1

as we know sin^2 theta + cos^2 theta = 1 so

1 + 2 sin theta * cos theta  = 1

2 sin theta * cos theta = 0

so let sin theta - cos theta = x

squaring both sides

sin^2 theta + cos^2 theta - 2 sin theta * cos theta = x^2

as 2 sin theta * cos theta = 0

sin^2 theta + cos^2 theta = x^2

so x^2 =1

so x = +- 1

hence proved

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