If \(\sin\theta-\mathrm{cosec}\,\theta=11\), what is the value of \(\sin^2\theta+\mathrm{cosec}^2\theta\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 123
\(\sin\theta\) and \(\mathrm{cosec}\,\theta\) are reciprocals, so their product is 1. Squaring a difference gives the sum of squares minus twice the product, so 2 is added back.
\((\sin\theta-\mathrm{cosec}\,\theta)^2=\sin^2\theta+\mathrm{cosec}^2\theta-2\)
\(121=\sin^2\theta+\mathrm{cosec}^2\theta-2\)
\(\sin^2\theta+\mathrm{cosec}^2\theta=123\)