Question

(cosec(90-Q)-sin(90-Q))(cosQ-sinQ)(tanQ+cotQ)=1
Please prove fast

Answer 1

Answer:

cot (90-Q)/tanQ+cosec (90-Q)sinQ/tan(90-Q)

= tanQ/tanQ+secQ*sinQ/cotQ

= 1+1/cosQ*sinQ/cosQ/sinQ

=1+1/cosQ*sin^{2}Q/cosQ

=1+sin^{2}Q/cos^{2}Q

=sec^{2}Q