If a cos 2x + b sin 2x = c has α and β as its roots, then prove that tan α + tan β = (c - a)/(c + a)

Question

If a cos 2x + b sin 2x = c has α and β as its roots, then prove that tan α + tan β = \(\frac{c-a}{c+a}\)

Answer 1

Therefore,

We know,

If m and n are roots of the equation ax² + bx + c = 0

then,

Product of the roots(mn) = \(\frac{c}{a}\)

Therefore,

If tan α and tan β are the roots of the equation