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Question

If sin a +sinß =0= cos a+cos ß, where 0<ß<a<2π, then which one of the following is correct?

a) a = π - ß

b) a = π + ß

c) a = 2π - ß

d) 2a = π + 2ß

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Solution

cosα+cosβ=0=sinα+sinβ=0
Squaring and adding we get cos(αβ)=1
α-β=cos inverse of - 1=π
​​​​​​


Therefore on rearranging, we get

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