MHT CET · Maths · Trigonometric Ratios & Identities
\(\cos x \cdot \cos 7 x-\cos 5 x \cdot \cos 13 x=\)
- A \(2 \cos ^{2} 6 x \cdot \cos 12 x\)
- B \(2 \sin ^{2} 6 x \cdot \cos 6 x\)
- C \(2 \sin 6 x \cdot \sin 12 x\)
- D \(2 \sin 6 x \cdot \cos 12 x\)
Answer & Solution
Correct Answer
(B) \(2 \sin ^{2} 6 x \cdot \cos 6 x\)
Step-by-step Solution
Detailed explanation
\(\cos x \cos 7 x-\cos 5 x \cos 13 x\)
\(\begin{array}{l}
=\frac{1}{2}(2 \cos x \cos 7 x-2 \cos 5 x \cos 13 x) \\
=\frac{1}{2}(\cos 8 x+\cos 6 x-\cos 18 x-\cos 8 x) \\
=\frac{1}{2}(\cos 6 x-\cos 18 x)=\frac{1}{2}[(-2) \sin 12 x \sin (-6 x)] \\
=\sin 12 x \sin 6 x=(2 \sin 6 x \cos 6 x) \sin 6 x \\
=2 \sin ^{2} 6 x \cos 6 x
\end{array}\)
\(\begin{array}{l}
=\frac{1}{2}(2 \cos x \cos 7 x-2 \cos 5 x \cos 13 x) \\
=\frac{1}{2}(\cos 8 x+\cos 6 x-\cos 18 x-\cos 8 x) \\
=\frac{1}{2}(\cos 6 x-\cos 18 x)=\frac{1}{2}[(-2) \sin 12 x \sin (-6 x)] \\
=\sin 12 x \sin 6 x=(2 \sin 6 x \cos 6 x) \sin 6 x \\
=2 \sin ^{2} 6 x \cos 6 x
\end{array}\)
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 \(z_1=5-2 i\) and \(z_2=3+i\), where \(i=\sqrt{-1}\), then \(\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)\) isMHT CET 2024 Easy
- Let \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) be three statements, then \([\mathrm{p} \rightarrow(\mathrm{q} \rightarrow \mathrm{r})] \leftrightarrow[(\mathrm{p} \wedge \mathrm{q}) \rightarrow \mathrm{r}]\) isMHT CET 2023 Easy
- If \(f(x)=\left\{\begin{array}{cl}\frac{\log (1+2 a x)-\log (1-b x)}{x}, & x \neq 0 \ k & , x=0\end{array}\right.\)
continuous at \(x=0\), then value of \(k\) isMHT CET 2012 Easy - The equation of a circle which has a tangent \(3 x+4 y=6\) and two normals given by \((x-1)(y-2)=0\) isMHT CET 2011 Medium
- If \(y=a \log x+b x^2+x\) has its extreme value at \(x=-1\) and \(x=2\), then the value of \(\mathrm{a}+\mathrm{b}\) isMHT CET 2024 Easy
- If \(y=2^{a x}\) and \(\left(\frac{d y}{d x}\right)_{x=1}=\log 256\), then \(a=\)MHT CET 2020 Easy
More PYQs from MHT CET
- The order and degree of the differential equation \(\frac{d^2 y}{d x^2}=\sqrt{\frac{d y}{d x}}\) are respectivelyMHT CET 2021 Easy
- \(
\int_{-1}^{1}\left[\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right] d x=
\)MHT CET 2020 Easy - Pyruvate is converted to Acetyl CoA by the process of ________.MHT CET 2025 Easy
- If \(2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0\) and \(\mathrm{y}=5 x^2 \mathrm{f}(x)\), then y is strictly increasing inMHT CET 2025 Hard
- Using differentiation, approximate value of at x = 2.99 is ….MHT CET 2019 Medium
- In amplitude modulation,MHT CET 2020 Easy