Establish the identity 1 cot2 theta sin2 theta 1 Rewrite t

Establish the identity. (1 + cot^2 theta) sin^2 theta = 1 Rewrite the left side expression by expanding the product.

Solution

we have given (1+cot²(theta))*sin²(theta)=1

LHS=(1+cot²(theta))*sin²(theta)

=cosec2(theta)*sin²(theta) since cosec2(theta)-cot²(theta)=1 implies 1+cot²(theta)=cosec2(theta)

=(1/sin²(theta))*sin²(theta) since cosec²(theta)=1/sin²(theta)

=1

=RHS

(1+cot²(theta))*sin²(theta)=1