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

1 Answer
sankarankalyanam
Nov 13, 2017

sin a / (1 + cos a)sina1+cosa

Explanation:

Multiply and divide by cot a + csc a + 1cota+csca+1

= ((1+cot a)^2 - csc ^2 a) / ((cot a + csc a)^2 - 1)=(1+cota)2−csc2a(cota+csca)2−1

(1 + cot^2a + 2cot a - 1 - cot^2a) / (cot^2a + csc^2a + 2cot a csc a -1)1+cot2a+2cota−1−cot2acot2a+csc2a+2cotacsca−1

= (2cot a) / (2 cot^2a + 2cot a csc a)=2cota2cot2a+2cotacsca

= (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)

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