QQuestion
Prove that:
(sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
ICSEClass XMathematicsHeights and Distances04 Mark2026 Moderate
✓Answer
L.H.S. (sec θ − cos θ)(cosec θ − sin θ)
= (\frac{1}{\cos \theta} − cos θ)(\frac{1}{\sin \theta} − sin θ)
= \frac{1-\cos^2 \theta}{\cos \theta} × \frac{1-\sin^2 \theta}{\sin \theta}
= \frac{\sin^2 \theta}{\cos \theta} × \frac{\cos^2 \theta}{\sin \theta}
= sin θ cos θ = R.H.S.
Hence, proved (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ.
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