Question

cosec alpha-cot alpha /cosec alpha+cot alpha=1-2 cosec alpha*cot alpha+2 cot^2 alpha​

Answer 1

Answer:

Answer:

1+\frac{cot^{2}\alpha}{1+cosec\alpha}=cosec\alpha1+

1+cosecα

cot

2

α

=cosecα

Step-by-step explanation:

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

1+cosecα

cot

2

α

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

1+cosecα

cosec

2

α−1

\*By algebraic identity:

cot²A = cosec²A-1 */

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

1+cosecα

cosec

2

α−1

2

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

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

(cosecα+1)

(cosecα−1)(cosecα+1)

After cancellation, we get

=1+ cosec\alpha - 1=1+cosecα−1

= cosec\alpha=cosecα

= RHS=RHS

Therefore,

1+\frac{cot^{2}\alpha}{1+cosec\alpha}=cosec\alpha1+

1+cosecα

cot

2

α

=cosecα