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Question

If sin α=45 and cos β=513, prove that cosαβ2=865

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Solution

We have,

sin α=45 and cos β=513 cos α=35 and sin β=1213 cos(αβ)=cos α cos β+sin α.sin β=35.513+45.1213=1565+4865=6365

Now,

cos(αβ2)=1+cos(αβ)2=1+63652=12865×2=6465=±865 cos (αβ2)=865


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