Quantitative Aptitude Ques 1320
Question: The value of $ \frac{1-{{\sin }^{2}}(\theta +16{}^\circ )}{1+{{\sin }^{2}}(\theta +31{}^\circ )} $ $ \times \frac{{{\cos }^{2}}(\theta +46{}^\circ )+{{\cos }^{2}}(\theta +16{}^\circ )}{cose{c^{2}}(\theta +76{}^\circ )-{{\cot }^{2}}(\theta +76{}^\circ )} $ $ \div ,{\sin (\theta +46{}^\circ )\tan (\theta +16{}^\circ )} $ for $ \theta =14{}^\circ $ is
Options:
A) $ -1 $
B) $ 0 $
C) $ \frac{1}{2} $
D) $ 1 $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \frac{1-{{\sin }^{2}}(\theta +16{}^\circ )}{1+{{\sin }^{2}}(\theta +31{}^\circ )}\times \frac{{{\cos }^{2}}(\theta +46{}^\circ )+{{\cos }^{2}}(\theta +16{}^\circ )}{ \begin{aligned} & cose{c^{2}}(\theta +76{}^\circ )-{{\cot }^{2}}(\theta +76{}^\circ ) \\ & \div {\sin (\theta +46{}^\circ )\tan (\theta +16{}^\circ )} \\ \end{aligned}} $
$ =\frac{1-{{\sin }^{2}}(14{}^\circ +16{}^\circ )}{1+{{\sin }^{2}}(14{}^\circ +31{}^\circ )}\times \frac{{{\cos }^{2}}(14{}^\circ +46{}^\circ )+{{\cos }^{2}}(14{}^\circ +16{}^\circ )}{cose{c^{2}}(14{}^\circ +76{}^\circ )-{{\cot }^{2}}(14{}^\circ +76{}^\circ )} $ $ \times \frac{1}{\sin (14{}^\circ +46{}^\circ )\tan (14{}^\circ +76{}^\circ )} $
$ [putting\theta =14{}^\circ ] $
$ =\frac{1-{{\sin }^{2}}30{}^\circ }{1+{{\sin }^{2}}45{}^\circ }\times \frac{{{\cos }^{2}}60{}^\circ +{{\cos }^{2}}30{}^\circ }{cose{c^{2}}90{}^\circ -{{\cot }^{2}}90{}^\circ }\times \frac{1}{\sin 60{}^\circ \tan 30{}^\circ } $
$ =\frac{1-{{( \frac{1}{2} )}^{2}}}{1+{{( \frac{1}{\sqrt{2}} )}^{2}}}\times \frac{{{( \frac{1}{2} )}^{2}}+{{( \frac{\sqrt{3}}{2} )}^{2}}}{{{(1)}^{2}}-{{( \frac{1}{\infty } )}^{2}}}\times \frac{1}{( \frac{\sqrt{3}}{2} )\cdot ( \frac{1}{\sqrt{3}} )} $
$ =\frac{1-\frac{1}{4}}{1+\frac{1}{2}}\times \frac{\frac{1}{4}+\frac{3}{4}}{1-0}\times \frac{1}{\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{3}}} $
$ =\frac{3/4}{3/2}\times \frac{1}{1}\times 2=\frac{1}{2}\times 2=1 $
BETA
