Prove that rac heta1− heta = extsec heta + exttan heta.

Here are the solutions to the problems.

Question 9:

a) Prove that $\frac{\cos\theta}{1-\sin\theta} = \sec\theta + \tan\theta$.

Step 1: Start with the left-hand side (LHS) of the equation.

$$\text{LHS} = \frac{\cos\theta}{1-\sin\theta}$$

Step 2: Multiply the numerator and denominator by the conjugate of the denominator, which is $1+\sin\theta$.

$$\text{LHS} = \frac{\cos\theta}{1-\sin\theta} \times \frac{1+\sin\theta}{1+\sin\theta}$$ $$$$