Prove the following identities: `(sintheta-sectheta)^2+(costheta-cos e ctheta)^2=(1-secthetacos e ctheta)^2`

Explanation

L.H.S `=(sin theta-sec theta)^{2}+(cos theta-{cosec} theta)^{2}`


` Cosec theta=frac{1}{sin theta} `


`sec theta=frac{1}{cos theta}`


`=(sin theta-frac{1}{cos theta})^{2}+(cos theta-frac{1}{sin theta})^{2}`


`=(frac{sin theta cos theta-1}{cos theta})^{2}+(frac{cos theta sin theta-1}{sin theta})^{2}`


`=(sin theta cos theta-1)^{2}(frac{1}{sin ^{2} theta}+frac{1}{cos ^{2} theta})`


`=(sin theta cos theta-1)^{2}(frac{cos ^{2} theta+sin ^{2} theta}{cos ^{2} theta sin ^{2} theta})`


` sin ^2 theta+cos ^{2} theta=1` (identity)


...