Question

Prove that 1+cos/sin -sin/1+cos = 2cot​

Answer 1

Answer:

 Let the angle be a

(1+cos a)/sin a - sin a/(1+cos a)

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

=cosec a  -  sin a/(1+cos a) +cot a

=(1 + cos a -sin^2 a)/sin a(1 + cos a) +cot a

=(cos^2 a + cos a)/sin a(1 + cos a)+cot a

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

=cos a/sin a + cot a       (1+cos a gets cancelled)

=cot a +cot a

=2cot a(proved)

Step-by-step explanation: