Question

Prove that: `(sin(180^0+theta)cos(90^0+theta)t a n(270^0-theta)cot(360^0-theta))/(sin(360^0-theta)cos(360^0+theta)cos e c(-theta)"sin"(270^0+theta))=1`

Answer 1

`L.H.S. = (sin(180^@+theta)cos(90^@+theta)tan(270^@-theta)cot(360^@-theta))/(sin(360^@-theta)cos(360^@+theta)cosec(-theta)sin(270^@+theta))`
`= (sin(theta)(-sin(theta))cot(theta)(-cot(theta)))/((-sin(theta))(cos(theta)(-cosec(theta)(-cos(theta))`
`=(sin^2thetacot^2theta)/(sinthetacosecthetacos^2theta)`
`=(sin^2theta(cos^2theta/sin^2theta))/(sintheta(1/sintheta)cos^2theta)`
`=cos^2theta/cos^2theta`
`=1 = R.H.S.`