SATHEE: Quantitative Aptitude Ques 1220

Quantitative Aptitude Ques 1220

Question: If $ \theta =\frac{1}{2}, $ then $ \frac{cose{c^{2}}\theta -{{\sec }^{2}}\theta }{cose{c^{2}}\theta +{{\sec }^{2}}\theta } $ is equal to

Options:

A) $ \frac{3}{5} $

B) $ \frac{1}{5} $

C) $ \frac{2}{5} $

D) $ \frac{4}{5} $

Show Answer

Answer:

Correct Answer: A

Solution:

$ \tan \theta =\frac{1}{2}=\frac{BC}{AB} $

$ \therefore $ $ BC=1 $ and $ AB=2 $ Now, $ {{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}} $

$ \Rightarrow $ $ {{(AC)}^{2}}={{(2)}^{2}}+{{(1)}^{2}} $

$ \Rightarrow $ $ AC=\sqrt{5} $

$ \therefore $ $ cosec\theta =\frac{AC}{BC}=\sqrt{5} $ and $ \sec \theta =\frac{AC}{AB}=\frac{\sqrt{5}}{2} $

$ \therefore $ $ \frac{cose{c^{2}}\theta -{{\sec }^{2}}\theta }{cose{c^{2}}\theta +{{\sec }^{2}}\theta }=\frac{{{(\sqrt{5})}^{2}}-{{( \frac{\sqrt{5}}{2} )}^{2}}}{{{(\sqrt{5})}^{2}}+{{( \frac{\sqrt{5}}{2} )}^{2}}} $ $ =\frac{5-\frac{5}{4}}{5+\frac{5}{4}}=\frac{15}{25}=\frac{3}{5} $

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Quantitative Aptitude Ques 1220

Question: If $ \theta =\frac{1}{2}, $ then $ \frac{cose{c^{2}}\theta -{{\sec }^{2}}\theta }{cose{c^{2}}\theta +{{\sec }^{2}}\theta } $ is equal to

Options:

Answer:

Solution:

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