If \sin\theta+\sin\alpha=m and \cos\theta+\cos\alpha=n, prove that: \frac{\sec(\theta+\alpha)}{2}=\frac{\sqrt{m^2+n^2}}{2}

Deven Livingston

Deven Livingston

Answered question

2022-04-21

If sinθ+sinα=m and cosθ+cosα=n, prove that:
sec(θ+α)2=m2+n22

Answer & Explanation

Ann Mathis

Ann Mathis

Beginner2022-04-22Added 11 answers

There must be something wrong in the Question.
m2+n24=2+2cos(θα)4=cos2θα2
Divide the first equation by the second to find tanθ+α2=mn
Now use sec2u=1+tan2u

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