Question

Simplified form of 1-sinx/cosx + cosx/1-sinx

Answer 1

Explanation:

Given

`(1 - sinx)/(cosx) + (cosx)/(1 - sinx) \\ = ((1 - sinx)^(2) + cos^(2)x )/(cosx(1 - sinx)) \\ = \frac{1 - 2sinx + sin ^(2)x + cos {}^(2)x}{cosx(1 - sinx)} \\ = (2 - 2sinx)/(cosx(1 - sinx)) \\ = (2(1 - sinx))/(cosx(1 - sinx)) \\ = (2)/(cosx) \\ = 2secx`

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