ExamBro
ExamBro
COMEDK · Maths · 8. Trigonometric Ratios & Identities

\(\left(\cos \dfrac{\pi}{12}-\sin \dfrac{\pi}{12}\right)\left(\tan \dfrac{\pi}{12}+\cot \dfrac{\pi}{12}\right)=\)

  1. A \(\sqrt{2}\)
  2. B \(2 \sqrt{2}\)
  3. C \(4 \sqrt{2}\)
  4. D \(\dfrac{1}{\sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \sqrt{2}\)

Step-by-step Solution

Detailed explanation

Let \(x = \dfrac{\pi}{12}\). The expression is \((\cos x - \sin x)(\tan x + \cot x)\). We know that \(\tan x + \cot x = \dfrac{\sin x}{\cos x} + \dfrac{\cos x}{\sin x} = \dfrac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \dfrac{1}{\sin x \cos x}\). Multiplying by \(2\) in the…