Question

costheta +sintheta =√2cos theta
show that costheta -sintheta = √2sintheta

question 15 please

Answer 1

cosx + sinx = √2cosx

Squaring both sides,
1 + 2 sinx cosx = 2 cos^2 x
2 sinx cosx = 2cos^2 x - 1. (1)

Let cosx - sinx = y

Squaring both sides,
1 - 2 sinx cosx = y^2
y^2 = 2 - 2cos^2 x. [From (1)]
y^2 = 2 (1 - cos^2 x)
y^2 = 2 sin^2 x
y = √2sinx

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