TS EAMCET · Maths · Trigonometric Ratios & Identities
If the period of the function \(f(x)=2 \cos (3 x+4)-3 \tan (2 x-3)+5 \sin (5 x)-7\) is \(k\), then
- A \(\sin \frac{k}{8}=\frac{1}{2}\)
- B \(\cos \frac{k}{6}=\frac{1}{\sqrt{2}}\)
- C \(\tan \frac{k}{3}=-\sqrt{3}\)
- D \(\sec \frac{k}{2}=2\)
Answer & Solution
Correct Answer
(C) \(\tan \frac{k}{3}=-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
Period of \(\cos (3 x+4)\) is \(\frac{2 x}{3}\) Period of \(\tan (2 x-3)\) is \(\frac{\pi}{2}\) Period of \(\sin 5 x\) is \(\frac{2 \pi}{5}\) Period of \(f(x)\) is L.C.M. of \(\frac{2 \pi}{3}, \frac{\pi}{2}, \frac{2 \pi}{5} \Rightarrow k=2 \pi\)…
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