Menu Close

Category: Trigonometry

Prove-that-the-area-of-any-quadrilateral-ABCD-is-s-a-s-b-s-c-s-d-abcd-cos-2-A-C-2-

Question Number 128178 by bemath last updated on 05/Jan/21 $$\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{quadrilateral}\:\mathrm{ABCD}\:\mathrm{is}\: \\ $$$$\:\sqrt{\left(\mathrm{s}−\mathrm{a}\right)\left(\mathrm{s}−\mathrm{b}\right)\left(\mathrm{s}−\mathrm{c}\right)\left(\mathrm{s}−\mathrm{d}\right)−\mathrm{abcd}\:\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{A}+\mathrm{C}}{\mathrm{2}}\right)}\:. \\ $$ Answered by mr W last updated on 05/Jan/21…

prove-that-sin-2x-2h-sin-2x-2cos-2x-h-sin-h-

Question Number 128130 by physicstutes last updated on 04/Jan/21 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{sin}\left(\mathrm{2}{x}\:+\:\mathrm{2}{h}\right)−\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{2cos}\left(\mathrm{2}{x}\:+{h}\right)\mathrm{sin}\:{h} \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{sin}{a}−\mathrm{sin}{b}\:=\:\mathrm{2sin}\left(\frac{{a}−{b}}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{{a}+{b}}{\mathrm{2}}\right)\:\left(\mathrm{1}\right) \\ $$$${a}\:=\:\mathrm{2}{x}+\mathrm{2}{h}\:\mathrm{and}\:{b}\:=\:\mathrm{2}{x} \\…

solve-for-x-in-0-x-2pi-sin-2x-sec-x-

Question Number 128094 by TITA last updated on 04/Jan/21 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\:\mathrm{in}\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi \\ $$$$\mathrm{sin}\:\mathrm{2x}=\mathrm{sec}\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 04/Jan/21 $$\mathrm{sin}\:\mathrm{2}{x}\:=\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:{x}\:={s} \\…

Given-25x-2-30x-7-0-has-the-roots-are-cos-and-cos-If-cos-cos-gt-0-then-the-value-of-tan-2-tan-2-

Question Number 128068 by benjo_mathlover last updated on 04/Jan/21 $$\:\mathrm{Given}\:\mathrm{25x}^{\mathrm{2}} −\mathrm{30x}+\mathrm{7}=\mathrm{0}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\mathrm{are}\:\mathrm{cos}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\beta.\:\mathrm{If}\:\mathrm{cos}\:\alpha−\mathrm{cos}\:\beta>\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\frac{\alpha+\beta}{\mathrm{2}}\right).\mathrm{tan}\:\left(\frac{\alpha−\beta}{\mathrm{2}}\right)\:=? \\ $$ Answered by bemath last updated on 04/Jan/21 $$\:\mathrm{let}\:\frac{\alpha+\beta}{\mathrm{2}}=\mathrm{x}\:\wedge\:\frac{\alpha−\beta}{\mathrm{2}}=\mathrm{y}…

Question-62431

Question Number 62431 by rajesh4661kumar@gamil.com last updated on 21/Jun/19 Answered by tanmay last updated on 21/Jun/19 $${asin}^{\mathrm{2}} \theta+{bcos}^{\mathrm{2}} \theta={c} \\ $$$${asin}^{\mathrm{2}} \theta+{b}\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right)={c} \\ $$$${sin}^{\mathrm{2}}…

Question-62347

Question Number 62347 by rajesh4661kumar@gamil.com last updated on 20/Jun/19 Answered by Kunal12588 last updated on 20/Jun/19 $$\frac{{csc}\:\theta\:−\:{sin}\:\theta}{{sec}\:\theta\:−\:{cos}\:\theta}\:=\:\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} } \\ $$$$\Rightarrow{cot}\:\theta\:\frac{\mathrm{1}−{sin}^{\mathrm{2}} \theta}{\mathrm{1}−{cos}^{\mathrm{2}} \theta}=\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} }…