Question

The value of Tan A + Cot A will be :

• A. Sin² A + Cot² A
• B. Sec A Cosec A
• C. Sin A Cos A
• D. 1

Hint:

The identity $\tan A + \cot A = \sec A \csc A$ is very useful in proving complex trigonometric identities.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To simplify trigonometric expressions involving $\tan$ and $\cot$, it is often easiest to convert them into $\sin$ and $\cos$ and then find a common denominator.
Step 2: Conversion and Expansion:
We know that $\tan A = \frac{\sin A}{\cos A}$ and $\cot A = \frac{\cos A}{\sin A}$.
$$\tan A + \cot A = \frac{\sin A}{\cos A} + \frac{\cos A}{\sin A}$$
Step 3: Finding Common Denominator:
$$\frac{\sin^2 A + \cos^2 A}{\cos A \sin A}$$
Since $\sin^2 A + \cos^2 A = 1$:
$$\frac{1}{\cos A \sin A} = \left(\frac{1}{\cos A}\right) \left(\frac{1}{\sin A}\right) = \sec A \csc A$$
Step 4: Final Answer:
The value of $\tan A + \cot A$ is Sec A Cosec A.