If tanθ =\(\frac{4}{3}\) , then the value of \(\frac{(3sinθ + 2cosθ)}{(3sinθ - 2cosθ)}\) is
Given: tanθ = \(\frac{4}{3}\)
We need to find the value of \(\frac{(3sinθ + 2cosθ)}{(3sinθ - 2cosθ)}\).
We can divide both the numerator and the denominator by cosθ:
\(\frac{(3sinθ + 2cosθ)}{(3sinθ - 2cosθ)} = \frac{3\frac{sinθ}{cosθ} + 2}{3\frac{sinθ}{cosθ} - 2}\)
Since tanθ = \(\frac{sinθ}{cosθ}\), we can substitute this into the expression:
\( \frac{3tanθ + 2}{3tanθ - 2} \)
Now, substitute the given value of tanθ = \(\frac{4}{3}\):
\( \frac{3(\frac{4}{3}) + 2}{3(\frac{4}{3}) - 2} = \frac{4 + 2}{4 - 2} = \frac{6}{2} = 3 \)
Therefore, the value of \(\frac{(3sinθ + 2cosθ)}{(3sinθ - 2cosθ)}\) is 3.
Why other options are incorrect:
- Option 1 (1/2): This is incorrect because it doesn't account for the given value of tanθ correctly.
- Option 2 (1\(\frac{1}{2}\)): This is also an incorrect calculation based on the provided data.
- Option 4 (-3): This would be the result if the signs in the numerator and denominator were reversed; however, the given expression does not have a negative in the numerator.
Similar Questions
If \(\tan A = \cot(2A - 30^{\circ})\), then what is the value of A?
If \(\sin A + \cos A = \sqrt{2} \sin A\), then what is the value of \(\tan A\)?
If \(\sin\theta = \dfrac{12}{13}\) and \(\theta \in \left(0, \tfrac{\pi}{2}\right)\), then what is the value of \(\tan\theta\)?
What is the value of \(\tan A + \cot A\) if \(\tan A = 2\)?
If \(\sin A + \cos A = \dfrac{5}{4}\), find \(\sin 2A\).
If \(\sin A = \dfrac{3}{5}\) and A lies in the second quadrant, find the value of \((\sin A + \cos A)^2\).
If \(\sin A = \dfrac{m}{n}\), then what is the value of \((1 + \tan^2 A)\)?
If \(\cot A = x + \dfrac{1}{x}\), find \(\cosec^2 A\).
If \(\sin^2 A - \cos^2 A = \dfrac{{1}}{{2}}\), find the value of \(\cos^2 A\).
If \(\cot A = x + \dfrac{{1}}{{x}}\), find \(\text{{cosec}}^2 A\).
Important Questions from Trigonometric Ratios and Identities
What is the ratio of the greatest to the smallest value of 2 – 2 sin x – sin 2x, 0 ≤ x ≤ (π/2)?
If sinθ = \(\frac{4}{5}\) , Find the value of sin3θ
If x, y are acute angles, where 0 < x + y < 90° and sin(3x - 40°) = cos (3y + 40°), then the value of tan (x + y) is equal to
What is (1 + cot θ - cosec θ)(1 + tan θ + sec θ) equal to?
If \(\sin \theta =\frac{3}{5}\) and \(\cos \theta =\frac{4}{5}\) , then the value of \(\frac{1+\tan \theta}{1-\cot \theta}\) is:
