Prove the identity: csc x - cot x = sinx/1+cosx
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
The identity csc x - cot x = sin x/(1+cos x) has to be proved.
Start from the left hand side
csc x - cot x
csc x = 1/ sin x and cot x = cos x/ sin x
=> 1/sin x - cos x/sin x
=> (1 - cos x)/sin x
=> (1 - cos x)(1 + cos x)/(sin x)*(1 + cos )
=> (1 - (cos x)^2)/(sin x)*(1 + cos )
=> (sin x)^2/(sin x)*(1 + cos )
=> sin x / (1 + cos )
which is the right hand side.
This proves csc x - cot x = sin x/(1+cos x)