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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(7 \cos \theta-\sin \theta=5\) and \(\tan \theta>0\), then \(\tan \theta=\)

  1. A \(\frac{7}{12}\)
  2. B \(\frac{3}{4}\)
  3. C \(\frac{4}{3}\)
  4. D \(\frac{12}{7}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{3}{4}\)

Step-by-step Solution

Detailed explanation

\(7 \cos \theta - \sin \theta = 5\) \(7 - \tan \theta = 5 \sec \theta\) \((7 - \tan \theta)^2 = 25 \sec^2 \theta\) \(49 - 14 \tan \theta + \tan^2 \theta = 25 (1 + \tan^2 \theta)\) \(49 - 14 \tan \theta + \tan^2 \theta = 25 + 25 \tan^2 \theta\)…