1cot2xcsc2x1sec2xSolutionwe have given 1cot2xcsc2x1sec2x LHS

1+cot^2x/csc^2x-1=sec^2x

Solution

we have given (1+cot²x)/(csc²x-1)=sec²x

LHS=(1+cot²x)/(csc²x-1)

=csc²x/cot²x since csc²x-cot²x =1 implies 1+cot²x=csc²x and csc²x-1=cot²x

=(1/sin²x)/(cos²x/sin²x)

=(1/sin²x)*(sin²x/cos²x)

=1/cos²x

=sec²x

the given equation is true