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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\cosh (x)=\frac{5}{4}\), then \(\cosh (3 x)\) is equal to

  1. A \(\frac{61}{16}\)
  2. B \(\frac{63}{16}\)
  3. C \(\frac{65}{16}\)
  4. D \(\frac{61}{63}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{65}{16}\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text {Given, } \cos h(x)=\frac{5}{4} \\ & \text { Now, } \cos h(3 x)=4 \cos h^3(x)-3 \cos h(x) \\ & =4\left(\frac{5}{4}\right)^3-3 \times \frac{5}{4}=\frac{125}{16}-\frac{15}{4} \\ & =\frac{125-60}{16}=\frac{65}{16}\end{aligned}\)