Question #c9323

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Answer 1 · 2017-11-21T15:25:07

Below.

Multiply both numerator and denominator by #1-sin(a)#

#( [1+sin(a)] * [1-sin(a)])/(cos(a) * [1-sin(a)])#

#= (1-sin^2(a))/(cos(a) [1-sin(a)])#

Convert #1-sin^2(a)# to #cos^2(a)#

#(cos^cancel(2)(a))/(cancel(cos(a))[1-sin(a)])#

#=cos(a)/(1-sin(a))#

Answer 2 · 2017-11-21T18:04:51

Please see Explanation.

We have, #1-sin^2a=cos^2a.#

#:. (1+sina)(1-sina)=(cosa)(cosa).#

#:. (1+sina)/cosa=cosa/(1-sina).#