Class 10 Maths Introduction to Trigonometry questions with solutions

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Solution

Q.
If tan θ = 3/4, evaluate $\frac{(1 + \sin θ) (1 - \sin θ)}{(1 + \cos θ) (1 - \cos θ)}$

Ans.
(16/9)

$\tan θ = \frac{3}{4} \Rightarrow \cot θ = \frac{4}{3}$

$\frac{(1 + \sin θ) (1 - \sin θ)}{(1 + \cos θ) (1 - \cos θ)} = \frac{1 - \sin^{2} θ}{1 - \cos^{2} θ} = \frac{\cos^{2} θ}{\sin^{2} θ} = \cot^{2} θ = {(\frac{4}{3})}^{2} = \frac{16}{9}$

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