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#