Question

b. cot x (sec x + tan x) = csc x + 1

Explanation:

Step1: Expand left-hand side (LHS)

$\cot x \sec x + \cot x \tan x$

Step2: Rewrite in sine/cosine terms

$\frac{\cos x}{\sin x} \cdot \frac{1}{\cos x} + \frac{\cos x}{\sin x} \cdot \frac{\sin x}{\cos x}$

Step3: Simplify each term

$\frac{1}{\sin x} + 1$

Step4: Rewrite using cosecant identity

$\csc x + 1$

Step5: Match to right-hand side (RHS)

$\csc x + 1 = \csc x + 1$

Answer:

The identity $\cot x (\sec x + \tan x) = \csc x + 1$ is verified.