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Category: Trigonometry

sin-x-cos-x-a-pi-4-x-pi-2-Which-statement-is-correct-1-sin-2-x-cos-2-x-1-2-3-2a-2-a-4-2-sin-4-x-cos-4-x-1-8-3a-4-6a-2-5-3-sin-2x-1-a-2-2-

Question Number 11456 by Joel576 last updated on 26/Mar/17 $$\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:{a},\:\:\frac{\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{Which}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}\:+\:\mathrm{2}{a}^{\mathrm{2}} \:−\:{a}^{\mathrm{4}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}^{\mathrm{4}} \:{x}\:+\:\mathrm{cos}^{\mathrm{4}} \:{x}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{3}{a}^{\mathrm{4}} \:+\:\mathrm{6}{a}^{\mathrm{2}} \:+\:\mathrm{5}\right) \\…

k-0-n-1-sec-2-kpi-n-n-2-

Question Number 142393 by qaz last updated on 31/May/21 $$\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\mathrm{sec}^{\mathrm{2}} \left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)=\mathrm{n}^{\mathrm{2}} ……??? \\ $$ Answered by mindispower last updated on 31/May/21 $$=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}}…

ABCD-is-a-cyclic-quad-and-the-diagonal-AC-and-BD-intersect-at-H-DAC-41-and-AHB-70-calulate-ACB-

Question Number 11301 by tawa last updated on 19/Mar/17 $$\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quad}\:\mathrm{and}\:\mathrm{the}\:\mathrm{diagonal}\:\mathrm{AC}\:\mathrm{and}\:\mathrm{BD}\:\mathrm{intersect}\:\mathrm{at}\:\mathrm{H}.\: \\ $$$$\bigtriangleup\mathrm{DAC}\:=\:\mathrm{41}°\:\mathrm{and}\:\bigtriangleup\mathrm{AHB}\:=\:\mathrm{70}°.\:\mathrm{calulate}\:\:\bigtriangleup\mathrm{ACB} \\ $$ Commented by sandy_suhendra last updated on 20/Mar/17 $$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\angle\mathrm{DAC},\:\angle\mathrm{AHB}\:\mathrm{and}\:\angle\mathrm{ACB}? \\ $$ Answered…

Find-max-amp-min-of-function-f-x-4tan-x-3cot-x-

Question Number 142167 by iloveisrael last updated on 27/May/21 $$\:\:\:{Find}\:{max}\:\&\:{min}\:{of}\:{function} \\ $$$$\:\:{f}\left({x}\right)=\mathrm{4tan}\:{x}+\mathrm{3cot}\:{x} \\ $$ Answered by MJS_new last updated on 27/May/21 $$−\infty<\mathrm{tan}\:{x}\:<+\infty\:\Rightarrow\:\mathrm{no}\:\mathrm{absolute}\:\mathrm{min},\:\mathrm{max} \\ $$$${g}\left({t}\right)=\mathrm{4}{t}+\frac{\mathrm{3}}{{t}} \\…

how-that-tan2x-2tanx-1-tan-2-x-

Question Number 76495 by mathocean1 last updated on 27/Dec/19 $$\mathrm{how}\:\mathrm{that} \\ $$$$\mathrm{tan2}{x}=\frac{\mathrm{2}{tanx}}{\mathrm{1}−{tan}^{\mathrm{2}} {x}} \\ $$ Commented by mathmax by abdo last updated on 27/Dec/19 $${due}\:{to}\:{formula}\:\:{tan}\left(\mathrm{2}{x}\right)={tan}\left({x}+{x}\right)\:=\frac{{tanx}+{tanx}}{\mathrm{1}−{tanx}.{tanx}}…

If-cos-1-sin-a-a-pi-2-2kpi-So-tan-2-A-a-a-1-D-a-1-a-1-B-1-a-1-E-a-a-1-C-a-1-a

Question Number 10955 by Joel576 last updated on 04/Mar/17 $$\mathrm{If}\:\:\frac{\mathrm{cos}\:\theta}{\mathrm{1}\:−\:\mathrm{sin}\:\theta}\:=\:{a}\:\:\:\:\:\:\:\:\:\:\:{a}\:\neq\:\frac{\pi}{\mathrm{2}}\:+\:\mathrm{2}{k}\pi \\ $$$$\mathrm{So},\:\:\mathrm{tan}\:\frac{\theta}{\mathrm{2}}\:=\:… \\ $$$$\left(\mathrm{A}\right)\:\:\frac{{a}}{{a}\:+\:\mathrm{1}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\:\frac{{a}\:+\:\mathrm{1}}{{a}\:−\:\mathrm{1}} \\ $$$$\left(\mathrm{B}\right)\:\:\frac{\mathrm{1}}{{a}\:+\:\mathrm{1}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:\:\frac{{a}}{{a}\:−\:\mathrm{1}} \\ $$$$\left(\mathrm{C}\right)\:\:\frac{{a}\:−\:\mathrm{1}}{{a}\:+\:\mathrm{1}} \\ $$ Answered by ajfour last updated…