1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Find the value of the following. (i) $\frac{\mathrm{sin}50°}{\mathrm{cos}40°}+\frac{\mathrm{cos}ec40°}{sec50°}-4\mathrm{cos}50°.\mathrm{cos}ec40°$

Open in App
Solution

## $\frac{\mathrm{sin}50°}{\mathrm{cos}40°}+\frac{\mathrm{cosec}40°}{\mathrm{sec}50°}-4\mathrm{cos}50°.\mathrm{cosec}40°\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{sin}\left(90-40\right)°}{\mathrm{cos}40°}+\frac{\mathrm{cosec}\left(90-50\right)°}{\mathrm{sec}50°}-4\mathrm{cos}\left(90-40\right)°\mathrm{cosec}40°\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{cos}40°}{\mathrm{cos}40°}+\frac{\mathrm{sec}50°}{\mathrm{sec}50°}-4\mathrm{sin}40°\mathrm{cosec}40°\left[\because \mathrm{cosec}\left(90-\mathrm{\theta }\right)=\mathrm{sec}\mathrm{\theta }\right]&\left[\mathrm{sin}\left(90-\mathrm{\theta }\right)=\mathrm{cos}\mathrm{\theta }\right]\phantom{\rule{0ex}{0ex}}=1+1-4\phantom{\rule{0ex}{0ex}}=-2$

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Introduction to Trigonometry
MATHEMATICS
Watch in App
Join BYJU'S Learning Program