If \(tan x = -3 4 \) and \( 3π 2 , then the value of sin 2x is

sin 2x &= 2 tan x/1 + tan 2 x \\ &= 2 × -3/4 1 + (-3/4) 2 \\ &= -3/2 16 + 9/16 \\ &= -3/2 × 16/25 = -24/25

If <span class=

\(tan x = -3 4 \) and \(tan x =... - Solved | MCA Prep" /> \(tan x = -3 4 \) and \(tan x =... - Solved | MCA Prep" /> \(tan x = -3 4 \) and

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Question 16

Mathematics Differentiation Hard

If <span class="math-tex">\(\tan x = \dfrac{-3}{4}\)</span> and <span class="math-tex">\(\dfrac{3\pi}{2}< x < 2\pi\)</span>, then the value of sin 2x is

(A) 7/25

(B) -7/25

(C) 24/25

(D) -24/25

✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\begin{aligned} \sin 2x &= \frac{2 \tan x}{1 + \tan^2 x} \\ &= \frac{2 \times \frac{-3}{4}}{1 + \left(\frac{-3}{4}\right)^2} \\ &= \frac{\frac{-3}{2}}{\frac{16 + 9}{16}} \\ &= \frac{-3}{2} \times \frac{16}{25} = \frac{-24}{25} \end{aligned}

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