Question

Assertion (A): If \((\tan \theta+\cot \theta)=n\) then \(\tan ^{2} \theta+\cot ^{2} \theta=n^{2}\).

Reason (R): \(\cot \theta=\frac{1}{\tan \theta}\).

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. Squaring the given relation gives \(\tan^{2}\theta+\cot^{2}\theta+2\tan\theta\cot\theta=n^{2}\). Since \(\tan\theta\cot\theta=1\), the sum of squares is \(n^{2}-2\), not \(n^{2}\).

Step 2 – Reason: R is true; cotangent is the reciprocal of tangent.