if a cos 2Φ + b sin 2Φ =c has p & q as its solutions, then prove thattan p + tan q =2b/a+c & tan p * tan q = c-a/a+c.

Dear nishant

a cos 2Φ + b sin 2Φ =c

a(1-tan²Φ)/(1+tan²Φ)   +  b (2tanΦ)/(1+tan²Φ) =c

 tan²Φ(a+c)  +tanΦ(-2b) +(c-a)=0

now tan p  and tanq  are the solution of this equation

tanp + tanq = 2b/(a+c)

tanp*tanq = (c-a)/(c+a)

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