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Find maximum value fo: cos^2 x(pi/3-x) – cos^2 (pi/3+x) is

Find maximum value fo: cos^2 x(pi/3-x) – cos^2 (pi/3+x) is

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
2cospi/3cosxsinpi/3sinx
jagdish singh singh
173 Points
5 years ago
\hspace{-0.7cm}f(x)=\cos^2\left(\frac{\pi}{3}-x\right)-\cos^2\left(\frac{\pi}{3}+x\right)=\sin^2\left(\frac{\pi}{3}+x\right)-\sin^2\left(\frac{\pi}{3}-x\right)$\\\\\\Using $\sin^2A-\sin^2 B=\sin(A+B)\sin(A-B)$\\\\\\ $f(x)=\sin(120^0)\sin(2x)=\frac{\sqrt{3}}{2}\sin(2x)\leq \frac{\sqrt{3}}{2}$ at $x=\frac{(4n+1)\pi}{4},n\in \mathbb{Z}$

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