How do you verify $(-1) / (tanx - secx) = (1 + sinx) / (cosx)$ ?

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Answer 1 · 2015-11-04T05:04:21

Verify trig expression.

Develop the left side.

$- 1/((sin x)/(cos x) - 1/(cos x)) = - ((cos x)/(sin x - 1)) = (cos x)/(1 - sin x)$

$= ((cos x)(1 + sin x))/((1- sin x)(1 + sin x)) =$
$= ((cos x) (1 + sin x))/( 1- sin^2 x) = ((cos x)(1 + sin x))/cos^2 x$
$= (1 + sin x)/(cos x)$

How do you verify (-1) / (tanx - secx) = (1 + sinx) / (cosx) (-1) / (tanx - secx) = (1 + sinx) / (cosx)?