AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \frac{5 \pi}{16} \sin \frac{7 \pi}{16}\) is equal to
- A \(\frac{\sqrt{2}}{16}\)
- B \(\frac{1}{8}\)
- C \(\frac{1}{16}\)
- D \(\frac{\sqrt{2}}{32}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{2}}{16}\)
Step-by-step Solution
Detailed explanation
We have, \(\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \frac{5 \pi}{16} \sin \frac{7 \pi}{16}\) \(=\sin \frac{\pi}{16} \sin \frac{3 \pi}{16} \sin \left(\frac{\pi}{2}-\frac{3 \pi}{16}\right) \sin \left(\frac{\pi}{2}-\frac{\pi}{16}\right)\)…
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
- Let \(\alpha, \beta\) be two real number such that \(\pi < (\alpha-\beta) < 3 \pi\). If \(\sin \alpha+\sin \beta=\frac{-21}{65}\) and \(\cos \alpha+\cos \beta=\frac{-2}{65}\), then \(\cos \left(\frac{\beta-\alpha}{2}\right)=\)AP EAMCET 2022 Medium
- Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \(x^3-a x^2+a x-1=0\) is identical with this cubic equation, then ' \(a\) ' =AP EAMCET 2025 Hard
- \(\int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x=\)AP EAMCET 2025 Medium
- An urn \(A\) contains 3 white and 5 black balls. Another urn \(B\) contains 6 white and 8 black balls. A ball is picked from A at random and then transferred to \(B\). Then, a ball is picked at random from \(B\). The probability that it is a white ball isAP EAMCET 2010 Medium
- AP EAMCET 2021 Medium
- The equation of the directrix of parabola \(y^2-x+4 y+5=0\) isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- If \(f(2)=4\) and \(f^{\prime}(2)=1\), then
\[
\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}
\]
is equal toAP EAMCET 2008 Medium - If \(f(x)=x^4-2 x^3+3 x^2-a x+b\) is divided by \(x-1\) and \(x+1\), the remainders are 5 and 19, respectively. If \(f(x)\) is divided by \(x-2\). The remainder isAP EAMCET 2021 Medium
- The angle subtended by the normal chord at the point \((9,9)\) on the parabola \(y^2=9 x\), at the focus of the parabola isAP EAMCET 2017 Hard
- The solution of \(x \frac{d y}{d x}=y+x e^{y / x}\) with \(y(1)=0\) isAP EAMCET 2014 Easy
- \(\int e^x\left(\log x+\frac{1}{x^2}\right) d x=\)AP EAMCET 2023 Medium
- If \(\bar{a}=\bar{i}+\bar{j}, \bar{b}=2 \bar{j}-\bar{k}\) are two vectors such that \(\bar{r} \times \bar{a}=\bar{b} \times \bar{a}, \bar{r} \times \bar{b}=\bar{a} \times \bar{b}\), then the unit vector in the direction of \(\overline{\mathrm{r}}\) isAP EAMCET 2025 Medium