How do you use the half angle formula to prove $(Cos (θ/2) - Sin( θ/2))^2$ ?

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Answer 1 · 2017-02-10T08:34:53

$(cos(theta/2)-sin(theta/2))^2=1+sintheta$

It appears as if something has been left in the question as there is no equation in the question.

However, we are using the formulas $sinA=2sin(A/2)cos(A/2)$ and $sin^2A+cos^2A=1$ and arriving at a likely result.

$(cos(theta/2)-sin(theta/2))^2$

= $cos^2(theta/2)+sin^2(theta/2)+2cos(theta/2)sin(theta/2)$

= $1+sintheta$

Hope it helps.

How do you use the half angle formula to prove (Cos (θ/2) - Sin( θ/2))^2 (Cos (θ/2) - Sin( θ/2))^2?