AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}=\)
- A \(1\)
- B \(\sqrt{5}\)
- C \(\frac{1}{4}(\sqrt{5}+1)(\sqrt{10+2 \sqrt{5}})\)
- D \(\frac{1}{4}(\sqrt{5}-1)(\sqrt{10+2 \sqrt{5}})\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{4}(\sqrt{5}+1)(\sqrt{10+2 \sqrt{5}})\)
Step-by-step Solution
Detailed explanation
\(\sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}\) \(= \frac{\sin(4 \cdot \frac{\pi}{5} / 2) \sin((4+1)\frac{\pi}{5}/2)}{\sin(\frac{\pi}{5}/2)}\)…
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
- In a \(\triangle A B C\), the sides \(a, b, c\) are in A.P. if and only if \(r_1, r_2, r_3\) are inAP EAMCET 2020 Medium
- If \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) and \(\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}\) are defined by \(\mathrm{f}(\mathrm{x})=\mathrm{x}^3-\mathrm{x}\) and \(g(x)=\sin 2 x\), then the value of \(x \in(0,2 \pi)\) that satisfy \(\mathrm{f}(\mathrm{g}(\mathrm{x}))>0\), lie in the intervalAP EAMCET 2023 Medium
- A candidate takes three tests in succession and the probability of passing the first test is \(p\). The probability of passing each succeeding test is \(p\) or \(\frac{p}{2}\) according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, isAP EAMCET 2014 Easy
- The differential equation of the family \(y=a e^x+b x e^x+c x^2 e^x\) of curves, where \(a, b, c\) are arbitrary constants, isAP EAMCET 2009 Easy
- On an average if one out of 100 electric bulbs produced by a Company is found to be defective, then the probability that there are at least two defective bulbs in a consignment of 600 bulbs, isAP EAMCET 2017 Medium
- If are position vectors of respectively and if are mid points of sides and , then is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- A plane is making intercepts \(2,3,4\) on \(X, Y\) and \(Z\)-axes respectively. Another plane is passing through the point \((-1,6,2)\) and is perpendicular to the line joining the points \((1,2,3)\) and \((-2,3,4)\). Then angle between the two planes isAP EAMCET 2019 Hard
- Acceleration due to gravityAP EAMCET 2020 Easy
- The number of \(120^{\circ}, \mathrm{Cl}-\mathrm{P}-\mathrm{Cl}\) angles in phosphorus pentachloride areAP EAMCET 2020 Easy
- For any complex number \(z\), the minimum value of \(|z|+|z-1|\) isAP EAMCET 2022 Easy
- Let \(\bar{a}=2 \bar{i}+\bar{j}-2 \bar{k}\) and \(\bar{b}=\bar{i}+\bar{j}\) be two vectors. If \(\bar{c}\) is a vector such that \(\bar{a} \cdot \bar{c}=|\bar{c}|,|\bar{c}-\bar{a}|=2 \sqrt{2}\) and the angle between \(\bar{a} \times \bar{b}\) and \(\bar{c}\) is \(30^{\circ}\), then \(|(\bar{a} \times \bar{b}) \times \bar{c}|=\)AP EAMCET 2025 Hard
- The sides of a triangle inscribed in a given circle subtend angles at the center. The minimum value of the of and is equal toAP EAMCET 2021 Easy