Prove that (cos θ) / (1 - sin θ) = sec θ + tan θ.

May 21, 2026Mathematics

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May 21, 2026

Answer

\sec\theta + \tan\theta$.

Here are the solutions to the problems from the image.

9. PURE MATHEMATICS

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

Step 1: Start with the left-hand side (LHS) and multiply the numerator and denominator by the conjugate of the denominator. $LHS = \frac{\cos\theta}{1-\sin\theta}$ $LHS = \frac{\cos\theta}{1-\sin\theta} \times \frac{1+\sin\theta}{1+\sin\theta}$

Step 2: Expand the expression and use the identity $1 - \sin^2\

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Quick Answer

Start with the left-hand side (LHS) and multiply the numerator and denominator by the conjugate of the denominator.

Asked on May 21, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 21, 2026

Here are the solutions to the problems from the image. 9. PURE MATHEMATICS a) Prove that ()/(1-) = + . Step 1: Start with the left-hand side (LHS) and multiply the numerator and denominator by the conjugate of the denominator. LHS = ()/(1-) LHS = ()/(1-) × (1+)/(1+) Step 2: Expand the expression and use the identity $1 - ^2\