Question

xi).
cosec X (1+cos x​

Answer 1

Step-by-step explanation:

Given that :-

Cosec X ( 1+Cos X)

=>(1+Cos X)/SinX

=>(1/Sin X)+(Cos X/Sin X)

=>Cosec X+Cot X

(or)

Cosec X(1+Cos X)

=>(1+CosX)/Sin X

multiply and divide both numerator and the denominator with (1-Cos X)

=>((1+CosX)(1-CosX))/((Sin X)(1-Cos X))

=>(1-Cos² X)/(SinX(1-Cos X)

=>Sin²X/(Sin X)(1-Cos X)

=>Sin X/(1-Cos X)

CosecX(1+CosX) = CosecX+CotX = SinX/(1-CosX)