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Question

State whether the following statement is true or false.
If cosα+cosβ+cosγ=sinα+sinβ+sinγ=0, then :
cos2α+cos2β+cos2γ=sin2α+sin2β+sin2γ=0

A
True
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B
False
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Solution

The correct option is A True
Let Z=ei(α+β+γ)=0

Therefore, cosα+cosβ+cosγ=0 & sinα+sinβ+sinγ=0

Now,

Z2=0(Z=0)

therefore, e2i(α+β+γ)=0

or ei(2α+2β+2γ)=0

therefore, cos2α+cos2β+cos2γ=sin2α+sin2β+sin2γ=0

Hence the above statement is true.

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