Question

The value of \(tan^{-1}(\frac{cos(\frac{19π}{4})-1}{sin(\frac{π}{4})})\) is equal to

• A. \(-\frac{π}{4}\)
• B. \(-\frac{5π}{12}\)
• C. \(-\frac{3π}{8}\)
• D. \(-\frac{4π}{9}\)

Hint:

Reduce 19pi/4 to a simple angle and recognise tan(3pi/8) = 1 + sqrt 2.

Answer 1

The Correct Option is C

Step 1: Simplify angle
$19\pi/4 - 4\pi = 3\pi/4$.

Step 2: Fraction
Numerator is $-\frac{1}{\sqrt2} - 1$, denominator is $\frac{1}{\sqrt2}$, so the ratio is $-1 - \sqrt2$.

Step 3: Identify
$\tan(3\pi/8) = \sqrt2 + 1$, so the inverse tangent is $-3\pi/8$. Option (C).

Final Answer:
Option (C). \[ \boxed{-\frac{3\pi}{8}} \]