AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(7 \cos \theta-\sin \theta=5\) and \(\tan \theta>0\), then \(\tan \theta=\)
- A \(\frac{7}{12}\)
- B \(\frac{3}{4}\)
- C \(\frac{4}{3}\)
- D \(\frac{12}{7}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(7 \cos \theta - \sin \theta = 5\) \(7 - \tan \theta = 5 \sec \theta\) \((7 - \tan \theta)^2 = 25 \sec^2 \theta\) \(49 - 14 \tan \theta + \tan^2 \theta = 25 (1 + \tan^2 \theta)\) \(49 - 14 \tan \theta + \tan^2 \theta = 25 + 25 \tan^2 \theta\)…
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