Question Number 81471 by jagoll last updated on 13/Feb/20 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{tan}\:\left(\mathrm{x}\right)\:=\:\mathrm{sinh}\:\left(\mathrm{y}\right)\:\mathrm{if}\:\mathrm{sin}\:\left(\mathrm{x}\right)= \\ $$$$\mathrm{tanh}\:\left(\mathrm{y}\right). \\ $$ Commented by john santu last updated on 13/Feb/20 $$\Rightarrow\mathrm{sin}\:\left(\mathrm{x}\right)=\mathrm{tanh}\:\left(\mathrm{y}\right)…
Question Number 15894 by Tinkutara last updated on 15/Jun/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:{ABC}\:\mathrm{be}\:\mathrm{in} \\ $$$$\mathrm{A}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{c}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:−\:{ab} \\ $$$$\left(\mathrm{2}\right)\:{b}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:{ac} \\ $$$$\left(\mathrm{3}\right)\:{a}^{\mathrm{2}} \:=\:{b}^{\mathrm{2}}…
Question Number 15893 by Tinkutara last updated on 15/Jun/17 $$\mathrm{In}\:\Delta{ABC},\:\mathrm{sides}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:{px}^{\mathrm{2}} \:+\:{qx}\:−\:{r}\:=\:\mathrm{0}.\:\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{area}\:\mathrm{of}\:\Delta{ABC}\:\mathrm{is} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{p}\left(\mathrm{4}{pq}\:−\:{p}^{\mathrm{3}} \:−\:\mathrm{8}{r}\right)} \\ $$ Answered by RasheedSoomro last…
Question Number 15888 by Tinkutara last updated on 15/Jun/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{in}\:\Delta{ABC},\:{a}^{\mathrm{3}} \:\mathrm{cos}\:\left({B}\:−\:{C}\right)\:+ \\ $$$${b}^{\mathrm{3}} \:\mathrm{cos}\:\left({C}\:−\:{A}\right)\:+\:{c}^{\mathrm{3}} \:\mathrm{cos}\:\left({A}\:−\:{B}\right)\:=\:\mathrm{3}{abc} \\ $$ Answered by ajfour last updated on 15/Jun/17 Commented…
Question Number 15828 by Tinkutara last updated on 14/Jun/17 $$\mathrm{In}\:\mathrm{a}\:\Delta{ABC},\:\mathrm{let}\:{M}_{{a}} ,\:{M}_{{b}} \:\mathrm{and}\:{M}_{{c}} \:\mathrm{denote} \\ $$$$\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{medians}, \\ $$$${s}\:=\:\frac{{M}_{{a}} \:+\:{M}_{{b}} \:+\:{M}_{{c}} }{\mathrm{2}}\:\:\mathrm{and}\:\Delta\:=\:\mathrm{ar}\left(\Delta{ABC}\right). \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\Delta\:=\:\frac{\mathrm{4}}{\mathrm{3}}\sqrt{{s}\left({s}\:−\:{M}_{{a}} \right)\left({s}\:−\:{M}_{{b}}…
Question Number 15824 by Tinkutara last updated on 18/Jun/17 $$\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…