Question

If cos θ = `3/5` , show that `((sin theta - cot theta ))/(2tan theta)=3/160`

Answer 1

LHS = `((sin theta - cot theta ))/(2tantheta)`

=`(sin theta costheta /sintheta )/(2(sintheta/costheta))`

=`((sin^2theta - costheta)/sintheta)/((2 sintheta/costheta))`

=` (costheta(sin^2theta-costheta))/(2sin^2theta)`

=`(costheta (1-cos^2theta-costheta))/(2(1-cos^2theta))`

=`(3/5[1-(3/5)^2-3/5])/(2[1-(3/5)^2])`

=`(3/5(1/1-9/25-3/5))/(2(1-9/25))`

=`(3/5((25-9-15)/25))/(2((25-9)/25))`

=`(3/5(1/25))/(2(16/25))`

=`3/(5xx2xx16)`

=`3/160`

= RHS