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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sin \left(5 x+\frac{\pi}{4}\right)=0\), then \(x\) is equal to

  1. A \(\frac{-\pi}{20}+\frac{\pi}{2} n(n \in z)\)
  2. B \(\frac{\pi}{20}+\frac{\pi}{5} n(n \in z)\)
  3. C \(\frac{-\pi}{5}+\frac{\pi}{5} n(n \in z)\)
  4. D \(\frac{-\pi}{20}+\frac{\pi}{5} n(n \in z)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{-\pi}{20}+\frac{\pi}{5} n(n \in z)\)

Step-by-step Solution

Detailed explanation

\(\sin \left(5 x+\frac{\pi}{4}\right)=0=\sin n \pi(\because \sin n \pi=0)\) where \(n \in Z\) \[ \begin{array}{rlrl} \Rightarrow & & 5 x+\frac{\pi}{4} & =n \pi \\ \Rightarrow & x & =\frac{1}{5}\left(n \pi-\frac{\pi}{4}\right)=\frac{n \pi}{5}-\frac{\pi}{20} \end{array} \]