Question

How do you prove `((sin^2x + 2cosx - 1)/(2 + cosx-cos^2x)) = 1/(1 + secx)`?

Answer 1

Left side Numerator:`(1 - cos^2 x + 2cos x -1) = -cos x(cos x - 2)`

Left side Denominator: `-(cos x + 1)(cos x - 2).`

Left side after simplification: `cos x/(cos x + 1)`

Right side:`1/(1 + 1/cos x) = cos x/(cos x + 1)`

Finally, left side = right side and the relation is proven.