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

Mathematics

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9. PURE MATHEMATICS

a) Prove that cos⁡θ1−sin⁡θ=sec⁡θ+tan⁡θ\frac{\cos\theta}{1-\sin\theta} = \sec\theta + \tan\theta.

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

    LHS=cos⁡θ1−sin⁡θ\text{LHS} = \frac{\cos\theta}{1-\sin\theta} LHS=cos⁡θ1−sin⁡θ×1+sin⁡θ1+sin⁡θ\text{LHS} = \frac{\cos\theta}{1-\sin\theta} \times \frac{1+\sin\theta}{1+\sin\theta}

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

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