Question

cosa/1-tana + sina/1-cota

Answer 1

cos a/1-tan a + sin a/1-cot
we know that tan=sin/cos and cot=cos/sin.
cos/1-sin/cos + sin/1-cos
so by taking lcm we get : cos a^2/1 - sin a + sin^2 a / 1-cos a
we also know that: cos^2a =1+sin^2a and sin^2a = 1+cos^2a
so now, 1+sin^2 a/1-sin a + 1+cos^2a/1-cos a 
using the identity: (a+b)(a-b)=a^2-b^2
we get: 1+sin a + 1 + cos a=2+sin a +cos a is the final ans.
 hope it helps.