Search any question & find its solution
Question:
Answered & Verified by Expert
$\sec 50^{\circ}+\tan 50^{\circ}$ is equal to
Options:
Solution:
2693 Upvotes
Verified Answer
The correct answer is:
$\tan 20^{\circ}+2 \tan 50^{\circ}$
$\sec 50^{\circ}+\tan 50^{\circ}$
$\begin{aligned}
& \Rightarrow \tan \left(70^{\circ}-20^{\circ}\right)=\frac{\tan 70^{\circ}-\tan 20^{\circ}}{1+\tan 70^{\circ} \tan 20^{\circ}} \\
& \Rightarrow \tan 50^{\circ}+\tan 70^{\circ} \tan 20^{\circ} \tan 50^{\circ}=\tan 70^{\circ}-\tan 20^{\circ} \\
& \Rightarrow \tan 50^{\circ}+\tan 50^{\circ}=\tan 70^{\circ}-\tan 20^{\circ} \\
& \left[ \tan 70^{\circ}=\cot 20^{\circ}\right] \\
& \Rightarrow 2 \tan 50^{\circ}+\tan 20^{\circ}=\tan 70^{\circ} \\
& \Rightarrow 2 \tan 50^{\circ}+\tan 20^{\circ}=\tan 50^{\circ}+\sec 50^{\circ} .
\end{aligned}$
$\begin{aligned}
& \Rightarrow \tan \left(70^{\circ}-20^{\circ}\right)=\frac{\tan 70^{\circ}-\tan 20^{\circ}}{1+\tan 70^{\circ} \tan 20^{\circ}} \\
& \Rightarrow \tan 50^{\circ}+\tan 70^{\circ} \tan 20^{\circ} \tan 50^{\circ}=\tan 70^{\circ}-\tan 20^{\circ} \\
& \Rightarrow \tan 50^{\circ}+\tan 50^{\circ}=\tan 70^{\circ}-\tan 20^{\circ} \\
& \left[ \tan 70^{\circ}=\cot 20^{\circ}\right] \\
& \Rightarrow 2 \tan 50^{\circ}+\tan 20^{\circ}=\tan 70^{\circ} \\
& \Rightarrow 2 \tan 50^{\circ}+\tan 20^{\circ}=\tan 50^{\circ}+\sec 50^{\circ} .
\end{aligned}$
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.