Question

$\cos {75}^{\circ }+\cot {75}^{\circ }$, when expressed in terms of angles between $0^{\circ }$ and ${30}^{\circ }$, becomes

• A. $\sin {15}^{\circ }+\tan {15}^{\circ }$
• B. $\sin 15+\cos 15$
• C. $\cos {15}^{\circ }+\tan {15}^{\circ }$
• D. None of these

Answer 1

Answer: (A)

$\sin {15}^{\circ }+\tan {15}^{\circ }$

We know that

$\cos A=\sin (90˚-A)$

$\cot A=\tan (90˚-A)$

$\text{cosec}A=\sec (90˚-A)$

Using these, we get

$\cos {75}^{\circ }=\sin (90˚-75˚)=\sin {15}^{\circ }$
$\cot {75}^{\circ }=\tan (90˚-75˚)=\tan {15}^{\circ }$

$\therefore \cos {75}^{\circ }+\cot {75}^{\circ }=\sin {15}^{\circ }+\tan {15}^{\circ }$.