Search any question & find its solution
Question:
Answered & Verified by Expert
If $3 \tan \theta+4=0$, where $(\pi / 2) < \theta < \pi$, then what is the value of $2 \cot \theta-5 \cos \theta+\sin \theta ?$
Options:
Solution:
1458 Upvotes
Verified Answer
The correct answer is:
$\frac{23}{10}$
As given, $3 \tan \theta+4=0 \Rightarrow \tan \theta=-\frac{4}{3}$
$\left[\theta\right.$ lies in second quadrant i.e., $\left.\frac{\pi}{2} < \theta < \pi\right]$
$\therefore \quad \cot \theta=-\frac{3}{4} \Rightarrow \cos \theta=-\frac{3}{5}$ and $\sin \theta=\frac{4}{5}$
Now, $2 \cot \theta-5 \cos \theta+\sin \theta$
$=-\frac{6}{4}+\frac{15}{5}+\frac{4}{5}=\frac{-30+60+16}{20}
$\left[\theta\right.$ lies in second quadrant i.e., $\left.\frac{\pi}{2} < \theta < \pi\right]$
$\therefore \quad \cot \theta=-\frac{3}{4} \Rightarrow \cos \theta=-\frac{3}{5}$ and $\sin \theta=\frac{4}{5}$
Now, $2 \cot \theta-5 \cos \theta+\sin \theta$
$=-\frac{6}{4}+\frac{15}{5}+\frac{4}{5}=\frac{-30+60+16}{20}
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.