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

May 20, 2026Mathematics

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May 20, 2026

Answer

\sec\theta + \tan\theta$.

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

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a) Prove that ()/(1-) = + . Step 1: Start with the left-hand side (LHS) of the equation.

Asked on May 20, 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 20, 2026

Here are the solutions to the problems. Question 9: a) Prove that ()/(1-) = + . Step 1: Start with the left-hand side (LHS) of the equation. LHS = ()/(1-) Step 2: Multiply the numerator and denominator by the conjugate of the denominator, which is 1+. LHS = ()/(1-) × (1+)/(1+) LHS =