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Category: Trigonometry

sin-2x-pi-4-sin-2x-pi-3-0-x-

Question Number 132347 by Study last updated on 13/Feb/21 $${sin}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{4}}\right)−{sin}\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{3}}\right)=\mathrm{0}\:\:\:{x}=? \\ $$ Answered by EDWIN88 last updated on 13/Feb/21 $$\mathrm{sin}\:\mathrm{X}−\mathrm{sin}\:\mathrm{Y}\:=\:\mathrm{2cos}\:\left(\frac{\mathrm{X}+\mathrm{Y}}{\mathrm{2}}\right)\mathrm{sin}\:\:\left(\frac{\mathrm{X}−\mathrm{Y}}{\mathrm{2}}\right) \\ $$$$\mathrm{where}\:\begin{cases}{\mathrm{X}=\mathrm{2x}+\frac{\pi}{\mathrm{4}}}\\{\mathrm{Y}=\mathrm{2x}+\frac{\pi}{\mathrm{3}}}\end{cases} \\ $$$$\mathrm{sin}\:\left(\mathrm{2x}+\frac{\pi}{\mathrm{4}}\right)−\mathrm{sin}\:\left(\mathrm{2x}+\frac{\pi}{\mathrm{3}}\right)=\mathrm{0} \\…

without-using-mathematical-tables-evaluate-sin-60-tan-30-cos-60-sin-30-cos-45-sin-45-sin-90-cos-45-sin-45-sin-60-cos-30-sin-30-

Question Number 66768 by John Kaloki Musau last updated on 19/Aug/19 $${without}\:{using}\:{mathematical}\:{tables} \\ $$$${evaluate} \\ $$$$\frac{\mathrm{sin}\:\mathrm{60}.\mathrm{tan}\:\mathrm{30}.\mathrm{cos}\:\mathrm{60}+\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}}{\mathrm{sin}\:\mathrm{90}.\mathrm{cos}\:\mathrm{45}.\mathrm{sin}\:\mathrm{45}−\mathrm{sin}\:\mathrm{60}.\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{30}} \\ $$ Commented by Tony Lin last updated on…

Question-132205

Question Number 132205 by Arijit last updated on 12/Feb/21 Commented by Arijit last updated on 12/Feb/21 $$\boldsymbol{\mathrm{Please}}\:\boldsymbol{\mathrm{Help}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}….. \\ $$ Answered by mathmax by abdo last…

Prove-tan-A-B-tan-A-sin-B-cos-A-cos-A-B-

Question Number 132081 by liberty last updated on 11/Feb/21 $$\mathrm{Prove}\:\mathrm{tan}\:\left(\mathrm{A}+\mathrm{B}\right)−\mathrm{tan}\:\mathrm{A}=\:\frac{\mathrm{sin}\:\mathrm{B}}{\mathrm{cos}\:\mathrm{A}\:\mathrm{cos}\:\left(\mathrm{A}+\mathrm{B}\right)} \\ $$ Answered by rs4089 last updated on 11/Feb/21 $${tan}\left({A}+{B}\right)−{tanA} \\ $$$$\frac{{sin}\left({A}+{B}\right)}{{cos}\left({A}+{B}\right)}−\frac{{sinA}}{{cosA}} \\ $$$$\frac{{sin}\left({A}+{B}\right).{cosA}−{sinA}.{cos}\left({A}+{B}\right)}{{cos}\left({A}+{B}\right).{cosA}} \\…

Trigonometry-What-is-the-minimum-value-of-3sin-x-4cos-x-10-3sin-x-4cos-x-10-

Question Number 132016 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{Trigonometry} \\ $$$$\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\sqrt{\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)\left(\mathrm{3sin}\:\mathrm{x}+\mathrm{4cos}\:\mathrm{x}−\mathrm{10}\right)}\:. \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\:\mathrm{consider}\:\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)−\mathrm{4cos}\:\mathrm{x}\right)\left(\left(\mathrm{3sin}\:\mathrm{x}−\mathrm{10}\right)+\mathrm{4cos}\:\mathrm{x}\right)= \\…