TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(3 \sin \theta+4 \cos \theta=3\) and \(\theta \neq(2 n+1) \frac{\pi}{2}\) then \(\sin 2 \theta=\)
- A \(\frac{336}{625}\)
- B \(-\frac{7}{25}\)
- C \(\frac{24}{25}\)
- D \(-\frac{336}{625}\)
Answer & Solution
Correct Answer
(D) \(-\frac{336}{625}\)
Step-by-step Solution
Detailed explanation
Let \(t = \tan \frac{\theta}{2}\). \(3 \frac{2t}{1+t^2} + 4 \frac{1-t^2}{1+t^2} = 3\) \(6t + 4(1-t^2) = 3(1+t^2)\) \(6t + 4 - 4t^2 = 3 + 3t^2\) \(7t^2 - 6t - 1 = 0\) \(t = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(7)(-1)}}{2(7)} = \frac{6 \pm \sqrt{36+28}}{14} = \frac{6 \pm 8}{14}\)…
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