How do I prove this trigonometric identity?

Question

#cos^2beta/(1-sinbeta)=1+sinbeta#

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Answer 1 · 2018-04-28T13:59:59

#cos^2beta/(1-sinbeta)=1+sinbeta#

#color(white)(#
Multiply and divide by #1+sinbeta#

#=>(cos^2beta(1+sinbeta))/((1-sinbeta)(1+sinbeta))#

#color(white)(#

#=>(cos^2beta(1+sinbeta))/(1-sin^2beta)#

#color(white)(#

#=>(cancelcos^2beta(1+sinbeta))/cancel(cos^2beta#
#color(white)(#

#->1+sinbeta#