One maximum point of \(\sin^{p}x\cos^{q}x\) is
Answer & explanation
Correct answer: option 1
Let \(f(x)=\sin^{p}x\cos^{q}x\hspace{6cm}\)
\(\begin{aligned}f^{\prime}(x)&=p\sin^{p-1}x\cos x\cos^{q}x-q\sin^{p}x\cos^{q-1}x\sin x\\ f^{\prime}(x)&=0\\ \tan^{2}x&=\frac{p}{q}\end{aligned}\)