If \(\tan\theta-\cot\theta=7\), then what is the value of \(\tan^2\theta+\cot^2\theta\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 51
\(\tan\theta\) and \(\cot\theta\) are reciprocals, so \(\tan\theta\cot\theta=1\). Squaring the difference brings in the sum of squares and twice this product.
\((\tan\theta-\cot\theta)^2=\tan^2\theta+\cot^2\theta-2\tan\theta\cot\theta\)
\(49=\tan^2\theta+\cot^2\theta-2\)
\(\tan^2\theta+\cot^2\theta=51\)