If α,β are two values of θ satisfying the equarion cosθa+sinθa=1c, then prove - cos(α+β2)cos(α−β2)=ca
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Solution
tanα2=t1,tanβ2=t−2 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)=a−ca+c or t1t2=p which is true