Question

1+cot alpha+cosec alpha/1-cot alpha+cosecalpha

Answer 1

Answer:

1+\frac{cot^{2}\alpha}{1+cosec\alpha}=cosec\alpha

Step-by-step explanation:

LHS=1+\frac{cot^{2}\alpha}{1+cosec\alpha}

=1+\frac{cosec^{2}\alpha-1}{1+cosec\alpha}

\*By algebraic identity:

cot²A = cosec²A-1 */

=1+\frac{cosec^{2}\alpha-1^{2}}{1+cosec\alpha}

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

=1+\frac{(cosec\alpha-1)(cosec\alpha+1)}{(cosec\alpha+1)}

After cancellation, we get

=1+ cosec\alpha - 1  

= cosec\alpha  

= RHS

Therefore,

1+\frac{cot^{2}\alpha}{1+cosec\alpha}=cosec\alpha