Class 10 Maths Introduction to Trigonometry questions with solutions, Prove that

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Solution

Q.
Prove that $\frac{\sin θ - \cos θ + 1}{\sin θ + \cos θ - 1} = \sec θ + \tan θ$

Ans.
$LHS = \frac{\tan θ - 1 + \sec θ}{\tan θ + 1 - \sec θ}$ (Dividing numerator and denominator by cos $θ$ )

$= \frac{\tan θ + \sec θ - 1}{\tan θ + 1 - \sec θ}$

$= \frac{\tan θ + \sec θ - (\sec^{2} θ - \tan^{2} θ)}{\tan θ + 1 - \sec θ}$

$= \frac{(\sec θ + \tan θ) (1 - \sec θ + \tan θ)}{\tan θ + 1 - \sec θ}$

$= \sec θ + \tan θ = RHS$

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