Question

If cosecФ + cotФ = q, show that cosecФ - cotФ = 1/q and hence find the values of sinФ and secФ.

Answer 1

bye a pythagorian identity.,
cosec^2-cot^2=1
so,we have....cosec+cot=q
                       multiplying both sides bye (cosec-cot) we get,
                       cosec^2-cot^2=q(cosec-cot)
                                 1=q(cosec-cot)
                           so,cosec-cot=1/q...proved
by solving simultaneous eqns.....sin=1/2(√q)(1/√1=q)

find sec by identiy.....sin^2+cos^2=1.....where cos=1/sec