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Question

If α,β are two values of θ satisfying the equarion cosθa+sinθa=1c, then prove -
cos(α+β2)cos(αβ2)=ca

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Solution

tanα2=t1,tanβ2=t2 are the roots of t quadratic b (a + c ) t2 - 2act + b (a - c ) = 0
Where t = \tan (θ/2) .
It is roots are t1,t2
By commpo and dividing om 2nd relation
2sin(α/2)sin(β/2)2cos(α/2)cos(β/2)=aca+c
or t1t2=p which is true

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