Question

If cosec a equal to root 2 find the value of cot A + sin a by 1 + Cos A

Answer 1

ANSWER -

The value is 1

STEP-BY-STEP EXPLANATION -

$\csc(a) = \sqrt{2} \\ \\ \csc(a) = \csc(45) \\ \\ a = 45 \: degrees \\ \\ \\ \frac{ \cot(a) + \sin(a)}{1 + \cos(a) } = \frac{ \cot(45) + \sin(45)}{1 + \cos(45) } \\ \\ = \frac{1 + \frac{1}{ \sqrt{2} } }{1 + \frac{1}{ \sqrt{2} } } \\ \\ \\ = 1$

KEY POINTS TO REMEMBER :-

☸️ cos 45 = 1/root2

☸️ cosec 45 = root 2

☸️ cot 45 = 1

☸️ sin 45 = 1/root 2