Question

(5 + cos x)*(5 - cos x) - sin^2 x - 24*cot^2 x * sin^2 x

Answer 1

`(5+cos x)(5-cos x)-sin^2 x-24cot^2 x.sin^2 x`

`=25-cos^2 x-sin^2 x-24[cos^2 x]/[sin^2 x].sin^2 x`

`=25-(sin^2 x+cos^2 x)-24cos^2 x`

`=25-1-24cos^2 x`

`=24-24cos^2 x`

Answer 2

\(=25-cos^2x-sin^2x-24.cot^2x.sin^2x\\ =25-\left(cos^2x+sin^2x\right)-24.\left(\dfrac{cos^2x}{sin^2x}\right).sin^2x\\ =25-1-24.cos^2x\\ =24-24.cos^2x\\ =24\left(1-cos^2x\right)\\ =24.\left(1-cosx\right)\left(1+cosx\right)\)