MHT CET · Maths · Trigonometric Equations
If \(3 \sin ^{2} x-8 \sin x+4=0, x \in\left(\frac{\pi}{2}, \pi\right)\), then \(\tan x=\)
- A \(-\frac{\sqrt{5}}{2}\)
- B \(\frac{2}{\sqrt{5}}\)
- C \(-\frac{2}{\sqrt{5}}\)
- D \(\frac{\sqrt{5}}{2}\)
Answer & Solution
Correct Answer
(C) \(-\frac{2}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
\(3 \sin ^{2} x-8 \sin x+4=0\)
\(\sin x-2)\left(\sin x-\frac{2}{3}\right)=0\)
\(\sin x=2\)
\(x\)
\(\sin x=\frac{2}{3}\)
\(\tan x=\frac{2}{\sqrt{5}}\) when \(x \in(\pi / 2, \pi)\)
\(\sin x-2)\left(\sin x-\frac{2}{3}\right)=0\)
\(\sin x=2\)
\(x\)
\(\sin x=\frac{2}{3}\)
\(\tan x=\frac{2}{\sqrt{5}}\) when \(x \in(\pi / 2, \pi)\)
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