Question #50ca2

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Answer 1 · 2017-03-27T21:05:25

$cos theta/(1-sintheta) = sec theta + tan theta$

Start from the first member:

$cos theta/(1-sintheta)$

multiply and divide by $(1+sin theta)$ :

$cos theta/(1-sintheta) = cos theta/(1-sintheta) (1+sin theta)/(1+sin theta)$

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

$cos theta/(1-sintheta) = cos theta(1+sintheta)/ cos^2 theta$

$cos theta/(1-sintheta) = (1+sintheta)/ cos theta$

$cos theta/(1-sintheta) = 1/cos theta +sintheta/ cos theta$

$cos theta/(1-sintheta) = sec theta + tan theta$