AP EAMCET · Maths · Trigonometric Equations
The most general value of \(\theta\) which satisfies both the equations \(\tan 8=-1\) and \(\cos \theta=\frac{1}{\sqrt{2}}\) is
- A \(n \pi+\frac{7 \pi}{4}\)
- B \(2 n \pi+\frac{7 \pi}{4}\)
- C \(n \pi+(-1)^n \frac{7 \pi}{4}\)
- D \(\frac{7 n \pi}{4}\)
Answer & Solution
Correct Answer
(B) \(2 n \pi+\frac{7 \pi}{4}\)
Step-by-step Solution
Detailed explanation
Given trigonometric equations are \(\tan \theta=-1\) and \(\cos \theta=\frac{1}{\sqrt{2}}\) \(\begin{array}{ll}\Rightarrow & \sin \theta=-1 / \sqrt{2} \\ \Rightarrow & \sin \theta=\sin \frac{7 \pi}{4} \\ \therefore & \theta=2 n \pi+\frac{7 \pi}{4}\end{array}\)
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