AP EAMCET · Maths · Trigonometric Equations
The general solution satisfying both the equations \(\sin x=-\frac{3}{5}\) and \(\cos x=-\frac{4}{5}\) is
- A \(\mathrm{x}=(2 \mathrm{n}+1) \pi+\operatorname{Tan}^{-1}\left(\frac{3}{4}\right), \mathrm{n} \in \mathrm{Z}\)
- B \(\mathrm{x}=2 \mathrm{n} \pi+\operatorname{Tan}^{-1}\left(\frac{3}{4}\right), \mathrm{n} \in \mathrm{Z}\)
- C \(\mathrm{x}=\mathrm{n} \pi+\operatorname{Tan}^{-1}\left(\frac{3}{4}\right), \mathrm{n} \in \mathrm{Z}\)
- D \(\mathrm{x}=\mathrm{n} \pi \pm \operatorname{Tan}^{-1}\left(\frac{3}{4}\right), \mathrm{n} \in \mathrm{Z}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{x}=(2 \mathrm{n}+1) \pi+\operatorname{Tan}^{-1}\left(\frac{3}{4}\right), \mathrm{n} \in \mathrm{Z}\)
Step-by-step Solution
Detailed explanation
\(\sin x \(\tan x = \frac{\sin x}{\cos x} = \frac{-3/5}{-4/5} = \frac{3}{4}\) Let \(\alpha = \operatorname{Tan}^{-1}\left(\frac{3}{4}\right)\). This is an acute angle. In the third quadrant, the principal value is \(\pi + \alpha\). The general solution is…
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