Question Number 15824 by Tinkutara last updated on 18/Jun/17 $$\mathrm{If}\:\mathrm{in}\:\mathrm{a}\:\Delta{ABC},\:\mathrm{cos}\:{A}\:+\:\mathrm{cos}\:{B}\:+\:\mathrm{cos}\:{C}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\Delta{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}. \\ $$ Answered by mrW1 last updated on 14/Jun/17 $$\mathrm{C}=\mathrm{180}−\left(\mathrm{A}+\mathrm{B}\right) \\…
Question Number 81354 by jagoll last updated on 12/Feb/20 $$\mathrm{given}\:\mathrm{y}\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{3}}−\mathrm{2x}\right)+\mathrm{2cos}\:\left(\frac{\pi}{\mathrm{12}}+\mathrm{x}\right)+\mathrm{1} \\ $$$$\mathrm{where}\:\mathrm{x}\:\in\left(\mathrm{0},\mathrm{2}\pi\right)\:\mathrm{has}\:\mathrm{maximum}\:\mathrm{and} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:\mathrm{is}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\mathrm{find}\:\mathrm{p}^{\mathrm{2}} −\mathrm{q}^{\mathrm{2}} \:? \\ $$$$\left(\mathrm{A}\right)\:−\mathrm{18}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:−\mathrm{16} \\ $$$$\left(\mathrm{C}\right)\:\frac{\mathrm{63}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{16} \\ $$ Commented…
Question Number 146877 by gsk2684 last updated on 16/Jul/21 $${if}\:{the}\:{sides}\:{a},{b},{c}\:{of}\:{a}\:{triangle}\:{ABC} \\ $$$${are}\:{in}\:{A}.{P}.\:{and}\:{if}\: \\ $$$$\mathrm{sin}\:{A}\:=\left(\mathrm{sin}\:{B}\:+\mathrm{sin}\:{C}\right)\mathrm{cos}\:\alpha \\ $$$$\mathrm{sin}\:{B}\:=\left(\mathrm{sin}\:{C}+\mathrm{sin}\:{A}\right)\mathrm{cos}\:\beta \\ $$$$\mathrm{sin}\:{C}\:=\left(\mathrm{sin}\:{A}\:+\mathrm{sin}\:{B}\right)\mathrm{cos}\:\gamma \\ $$$${then}\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\mathrm{tan}\:^{\mathrm{2}} \frac{\alpha}{\mathrm{2}}+\mathrm{tan}\:^{\mathrm{2}} \frac{\gamma}{\mathrm{2}} \\…
Question Number 146878 by gsk2684 last updated on 16/Jul/21 $${in}\:\Delta{ABC}\:{if}\:\mathrm{sin}\:^{\mathrm{2}} {A}\:\mathrm{sin}\:{B}\:\mathrm{sin}\:{C}+ \\ $$$$\mathrm{cos}\:{B}\mathrm{cos}\:{C}=\mathrm{1}\:{then}\:{the}\:{triangle}\:{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 146876 by gsk2684 last updated on 16/Jul/21 $${if}\:{the}\:{maximum}\:{value}\:{of}\: \\ $$$$\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{3cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:\frac{{x}}{\mathrm{2}}+\mathrm{cos}\:\frac{{x}}{\mathrm{2}}+\mathrm{3} \\ $$$${is}\:{a}+\sqrt{{b}}\:{then}\:{find}\:{a}+{b} \\ $$ Answered by liberty last updated on 16/Jul/21…
Question Number 146875 by gsk2684 last updated on 16/Jul/21 $${In}\:{a}\:{triangle}\:{ABC},\:{if}\: \\ $$$$\frac{\mathrm{sin}\:{A}}{\mathrm{5}−{x}}=\frac{\mathrm{sin}\:{B}}{\mathrm{3}{x}−\mathrm{1}}=\frac{\mathrm{sin}\:{C}}{\mathrm{2}{x}+\mathrm{5}}\:{then}\:{find} \\ $$$$\:{integral}\:{solutions}\:{x}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 146874 by gsk2684 last updated on 16/Jul/21 $${let}\:{the}\:{line}\:{joining}\:{through}\: \\ $$$${orthocenter}\:{and}\:{circumcenter}\: \\ $$$${of}\:{a}\:{triangle}\:{ABC}\:{is}\:{parallel}\:{to}\: \\ $$$${the}\:{base}\:{BC}\:{then}\:{find}\:\:\mathrm{tan}\:{B}.\mathrm{tan}\:{C} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 146868 by gsk2684 last updated on 16/Jul/21 $${if}\:\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{sec}\:{x}={a}+\mathrm{1}\:{has}\:{at}\:{least}\: \\ $$$${one}\:{solution}\:{then}\:{find}\:{the}\:{complete}\:{set} \\ $$$${of}\:{values}\:{of}\:\:'{a}'? \\ $$ Answered by Olaf_Thorendsen last updated on 16/Jul/21 $$\mathrm{tan}^{\mathrm{2}}…
Question Number 15786 by tawa tawa last updated on 13/Jun/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{7}}\right)\:−\:\mathrm{cos}\left(\frac{\mathrm{2x}}{\mathrm{7}}\right)\:+\:\mathrm{cos}\left(\frac{\mathrm{3x}}{\mathrm{7}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by tawa tawa last updated on 14/Jun/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{this}. \\…
Question Number 146850 by Apor_mu_calculus last updated on 16/Jul/21 $$ \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com