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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(x=\tan 15^{\circ}, y=\operatorname{cosec} 75^{\circ}\) and \(z=4 \sin 18^{\circ}\), then :

  1. A \(x < y < z\)
  2. B \(y < z < x\)
  3. C \(z < x < y\)
  4. D \(x < z < y\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x < y < z\)

Step-by-step Solution

Detailed explanation

\(\because \quad x=\tan 15^{\circ}=\tan\left(45^{\circ}-30^{\circ}\right)\) \(=\frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}\) \(=\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{(\sqrt{3}-1)^2}{3-1}\)…