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Category: Trigonometry

Question-134417

Question Number 134417 by faysal last updated on 03/Mar/21 Answered by som(math1967) last updated on 03/Mar/21 $$\frac{\mathrm{2}^{{n}−\mathrm{1}} \mathrm{2}{sin}\theta{cos}\theta.{cos}\mathrm{2}\theta…{cos}\mathrm{2}^{{n}−\mathrm{1}} \theta}{{sin}\theta} \\ $$$$\frac{\mathrm{2}^{{n}−\mathrm{2}} .\mathrm{2}{sin}\mathrm{2}\theta{cos}\mathrm{2}\theta.{cos}\mathrm{2}^{\mathrm{2}} \theta…..}{{sin}\theta} \\ $$$$\frac{\mathrm{2}^{{n}−\mathrm{3}}…

If-cosec-sec-and-cot-are-in-H-P-then-sin-tan-cos-

Question Number 3317 by rishabh last updated on 10/Dec/15 $$\mathrm{If}\:\mathrm{cosec}\:\theta,\:\mathrm{sec}\:\theta,\:\mathrm{and}\:\mathrm{cot}\:\theta\:\mathrm{are}\:\mathrm{in}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\frac{\mathrm{sin}\:\theta+\mathrm{tan}\:\theta}{\mathrm{cos}\:\theta}\:=\:? \\ $$ Answered by prakash jain last updated on 10/Dec/15 $$\frac{\mathrm{2}}{\mathrm{sec}\:\theta}=\frac{\mathrm{1}}{\mathrm{cosec}\:\theta}+\frac{\mathrm{1}}{\mathrm{cot}\:\theta}=\mathrm{sin}\:\theta+\mathrm{tan}\:\theta \\ $$$$\mathrm{2cos}\:\theta=\mathrm{sin}\:\theta+\mathrm{tan}\:\theta…

Two-arcs-having-their-centers-on-a-circle-are-cutting-each-other-at-a-single-point-inside-the-circle-and-thus-dividing-the-circle-in-four-regions-If-the-arcs-cut-each-other-in-a-b-amp-c-d-ratio

Question Number 68761 by Rasheed.Sindhi last updated on 15/Sep/19 $$\mathrm{Two}\:\boldsymbol{\mathrm{arcs}}\:\mathrm{having}\:\mathrm{their}\:\mathrm{centers}\:\mathrm{on}\:\mathrm{a} \\ $$$$\boldsymbol{\mathrm{circle}}\:\mathrm{are}\:\mathrm{cutting}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{a}\: \\ $$$$\mathrm{single}\:\mathrm{point}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{and}\:\mathrm{thus} \\ $$$$\:\mathrm{dividing}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{four}\:\mathrm{regions}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{arcs}\:\mathrm{cut}\:\mathrm{each}\:\mathrm{other}\:\mathrm{in}\:\boldsymbol{\mathrm{a}}:\boldsymbol{\mathrm{b}}\:\&\:\boldsymbol{\mathrm{c}}:\boldsymbol{\mathrm{d}}\: \\ $$$$\mathrm{ratios}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{between}\:\mathrm{four} \\ $$$$\mathrm{regions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{when}\:\mathrm{the}\:\mathrm{circle} \\…

find-sin-20-

Question Number 68673 by mr W last updated on 14/Sep/19 $${find}\:\boldsymbol{\mathrm{sin}}\:\mathrm{20}°=? \\ $$ Commented by MJS last updated on 15/Sep/19 $$\Rightarrow\:\mathrm{we}\:\mathrm{cannot}\:\mathrm{use}\:\mathrm{this}\:\mathrm{to}\:\mathrm{get}\:\mathrm{sin}\:\mathrm{1}°,\:\mathrm{because} \\ $$$$\mathrm{sin}\:\mathrm{3}°\:=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)\sqrt{\mathrm{5}+\sqrt{\mathrm{5}}}−\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{1}−\sqrt{\mathrm{5}}\right)\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)\sqrt{\mathrm{2}} \\ $$$$\mathrm{and}…

Solve-1-cos-x-1-cos-x-2sin-x-

Question Number 134165 by liberty last updated on 28/Feb/21 $$\mathrm{Solve}\:\sqrt{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\:+\:\sqrt{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}\:=\:\mathrm{2sin}\:\mathrm{x} \\ $$ Answered by EDWIN88 last updated on 28/Feb/21 $$\mathrm{square}\:\mathrm{both}\:\mathrm{sides} \\ $$$$\Leftrightarrow\:\mathrm{2}+\mathrm{2}\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x} \\…

sin-1-

Question Number 68482 by Maclaurin Stickker last updated on 11/Sep/19 $$\mathrm{sin}\:\mathrm{1}^{°} \:=\:? \\ $$ Commented by mr W last updated on 11/Sep/19 $$\mathrm{sin}\:\mathrm{1}^{°} \:=\:\mathrm{sin}\:\frac{\pi}{\mathrm{180}}\:\approx\frac{\pi}{\mathrm{180}}=\mathrm{0}.\mathrm{0174533} \\…