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

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Answer 1 · 2015-05-17T20:34:17

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.

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