Question

Answer correctly and only If you know!

Trigonometry!!!

●Find the value of cos 75°?​
●Find the value of sin 135° ?​
●$= \frac{ { \sin }^{2}48 }{ { \cos }^{2}48 } + 1 = ?$

No spam !!

​

Answer 1

${\huge {\underline {\mathfrak {\green {Answer}}}}}$

Solution 1❇

= cos 75°

= cos (45°+30°)

= cos 45°. cos 39° - sin45° . sin30°

= $\displaystyle\frac {1}{\sqrt{2}}.\displaystyle\frac {\sqrt {3}}{2}-\displaystyle\frac {1}{\sqrt{2}}.\displaystyle\frac {1}{2}$

= $\displaystyle\frac {\sqrt {3}}{2\sqrt{2}}-\displaystyle\frac {1}{2\sqrt{2}}$

=$\displaystyle\frac {\sqrt {3}-1}{2\sqrt{2}}$

Solution 2❇

= sin 135°

= sin (90+45°)

= sin 90.cos45+cos90.sin45

=$1 × \displaystyle\frac {1}{\sqrt{2}}+ 0×\displaystyle\frac {1}{\sqrt{2}}$

= $\displaystyle\frac {1}{\sqrt{2}}$

Solution 3❇

=$\frac{ { \sin }^{2}48 }{ { \cos }^{2}48 } + 1 = ?$

= ${ \tan}^{2} 48 + 1$

=${\sec}^{2}\:48°$

_________________..........