Simplify (1+cot^2 x)(cos2x +1)?

Answer 1

1 + Cot^2 x = Cosec^2 X = (1 / Sin X )^2 ------- (A)
Cos2X + 1 = 2Cos^2 X -------(B)

(A) x (B) = 2 (Cos^2 X ) / (Sin^2 X)
= 2 (Cos X / Sin X)^2
= 2(Cot^2 X)

is the answer

Hope you;re familiar with A & B statements... :)

Answer 2

Simplify (1 + cot²x)(cos2x + 1).

(1 + cot²x)(cos2x + 1) = (csc²x)[(2cos²x - 1) + 1]

= (csc²x)(2cos²x) = 2cos²x / sin²x = 2cot²x