SATHEE: Quantitative Aptitude Ques 1326

Quantitative Aptitude Ques 1326

Question: If $ x=a(\sin \theta +\cos \theta ), $ $ y=b(\sin \theta -\cos \theta ), $ then the value of $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} $ is

Options:

A) $ 0 $

B) $ 1 $

C) $ 2 $

D) $ -2 $

Show Answer

Answer:

Correct Answer: C

Solution:

Given, $ x=a(\sin \theta +cos\theta ) $ On squaring both sides, we get $ x^{2}=a^{2}({{\sin }^{2}}\theta +{{\cos }^{2}}\theta +2\sin \theta \cos \theta ) $ $ =a^{2}(1+2\sin \theta \cos \theta ) $ Similarly, $ y=b(\sin \theta -\cos \theta ) $

$ \Rightarrow $ $ y^{2}=b^{2}({{\sin }^{2}}\theta +{{\cos }^{2}}\theta -2\sin \theta \cos \theta ) $ $ =b^{2}(1-2\sin \theta \cos \theta ) $ Now, $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{a^{2}(1+2\sin \theta \cos \theta )}{a^{2}} $ $ +\frac{b^{2}(1-2\sin \theta \cos \theta )}{b^{2}} $ $ =1+2\sin \theta \cos \theta +1-2\sin \theta \cos \theta $ $ =2 $

Quantitative Aptitude Ques 1325

Quantitative Aptitude Ques 1327

Quantitative Aptitude Ques 1326

Question: If $ x=a(\sin \theta +\cos \theta ), $ $ y=b(\sin \theta -\cos \theta ), $ then the value of $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} $ is

Options:

Answer:

Solution:

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