AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cosh (x)=\frac{5}{4}\), then \(\cosh (3 x)\) is equal to
- A \(\frac{61}{16}\)
- B \(\frac{63}{16}\)
- C \(\frac{65}{16}\)
- D \(\frac{61}{63}\)
Answer & Solution
Correct Answer
(C) \(\frac{65}{16}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Given, } \cos h(x)=\frac{5}{4} \\ & \text { Now, } \cos h(3 x)=4 \cos h^3(x)-3 \cos h(x) \\ & =4\left(\frac{5}{4}\right)^3-3 \times \frac{5}{4}=\frac{125}{16}-\frac{15}{4} \\ & =\frac{125-60}{16}=\frac{65}{16}\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the smallest circle through the points of intersection of \(x^2+y^2=a^2\) and \(x \cos \alpha+y \sin \alpha=p, 0 < p < a\) is \(x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0\) then \(\lambda=\)AP EAMCET 2025 Medium
- If , then the value of is equal toAP EAMCET 2021 Easy
- If \(A\) and \(B\) are any two events such that \(P(\overline{A \cup B})=\frac{1}{6}, P(A \cap B)=\frac{1}{4}\) and \(P(\bar{A})=\frac{1}{4}\), then the events \(A\) and \(B\) areAP EAMCET 2017 Easy
- A plane \(\pi\) given by \(a x+b y+11 z+d=0\) is perpendicular to the planes \(2 x-3 y+z=4,3 x+y-z=5\) and the perpendicular distance from the origin to the plane \(\pi\) is \(\sqrt{6}\) units. If all the intercepts made by the plane \(\pi\) on the coordinate axes are positive, then \(d=\)AP EAMCET 2025 Hard
- A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected isAP EAMCET 2023 Medium
- If the lines are conjugate with respect to the circle thenAP EAMCET 2018 Medium
More PYQs from AP EAMCET
- \(\tanh ^{-1}\left(\frac{1}{2}\right)+\operatorname{coth}^{-1}(2)\) is equal toAP EAMCET 2013 Medium
- \(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)AP EAMCET 2024 Medium
- If, \(\Delta H>0\) and \(\Delta S>0\), the reaction can proceed spontaneously atAP EAMCET 2020 Easy
- If the primitive of is , then which among the following is true?AP EAMCET 2021 Easy
- If the direction cosines of two lines are such that \(2 l+m+2 n=0\) and \(3 l^2+5 m^2-11 n^2=0\), then the angle between the two lines isAP EAMCET 2017 Medium
- On a smooth inclined plane, a mass \(M\) is attached between two massless springs of force constant \(k\) each, as shown in the figure. The other ends of the springs are fixed to firm supports. The period of oscillation of the mass \(M\) is
AP EAMCET 2020 Hard