Question

Answer:

1+\frac{cot^{2}\alpha}{1+cosec\alpha}=cosec\alpha1+1+cosecαcot2α​=cosecα

Step-by-step explanation:

LHS=1+\frac{cot^{2}\alpha}{1+cosec\alpha}LHS=1+1+cosecαcot2α​

=1+\frac{cosec^{2}\alpha-1}{1+cosec\alpha}=1+1+cosecαcosec2α−1​

\*By algebraic identity:

cot²A = cosec²A-1 */

=1+\frac{cosec^{2}\alpha-1^{2}}{1+cosec\alpha}=1+1+cosecαcosec2α−12​

/* 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+cosecαcot2α​=cosecα

​

Answer 1

Step-by-step explanation:

The natural environment encompasses all living and non-living things occurring naturally, meaning in this case not artificial. The term is most often applied to the Earth or some parts of Earth...............

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