Question

Show that Sec^2theta +cosec^2theta is positive quantity.

Answer 1

I am using theta = x.

Let. t= sec^2(x)+cosec^2(x)……….(1)

t= 1+tan^2(x)+1+cot^2(x)

t=2+tan^2(x)+cot^2(x)

t= 2 + {tan^2(x)+cot^2(x)}

Therefore. t is greater than 2.

or. t can never be less than 2.

On putting the value of t from eqn. (1)

or. sec^2(x)+cosec^(x). can never be less than. 2. Answer.