[cot(a)-cosec(a)+1]/[cot(a)+cosec(a)-1]=?

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Answer 1 · 2017-11-13T10:56:40

#sin a / (1 + cos a)#

Multiply and divide by #cot a + csc a + 1#

#= ((1+cot a)^2 - csc ^2 a) / ((cot a + csc a)^2 - 1)#

#(1 + cot^2a + 2cot a - 1 - cot^2a) / (cot^2a + csc^2a + 2cot a csc a -1)#

#= (2cot a) / (2 cot^2a + 2cot a csc a)#

#= (cancel(2 cot a))/ (cancel(2 cot a)(cot a + csc a)#

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

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