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Author: Tinku Tara

If-asin-2-bcos-2-c-bsin-2-acos-2-d-and-atan-btan-then-prove-that-1-a-1-b-1-c-1-d-

Question Number 206500 by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{If}\:{a}\mathrm{sin}^{\mathrm{2}} \theta\:+\:{b}\mathrm{cos}^{\mathrm{2}} \theta\:=\:{c},\:{b}\mathrm{sin}^{\mathrm{2}} \phi\:+\:{a}\mathrm{cos}^{\mathrm{2}} \phi\:=\:{d} \\ $$$$\mathrm{and}\:{a}\mathrm{tan}\theta\:=\:{b}\mathrm{tan}\phi\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:=\:\frac{\mathrm{1}}{{c}}\:+\:\frac{\mathrm{1}}{{d}}\:. \\ $$ Answered by Berbere last updated…

If-x-log-3-x-1-log-3-x-3-Find-log-3-x-1-log-3-x-2-

Question Number 206501 by hardmath last updated on 16/Apr/24 $$\mathrm{If} \\ $$$$\mathrm{x}^{\boldsymbol{\mathrm{log}}_{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{1}} \:\:=\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}\:+\:\mathrm{3} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{2}} \:=\:? \\ $$ Commented by…

If-a-gt-b-gt-0-and-4a-2-b-2-4ab-Find-a-b-a-b-

Question Number 206477 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4ab} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{a}\:−\:\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{4}{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}}…

If-4-p-5-Find-2-3p-

Question Number 206473 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{4}^{\boldsymbol{\mathrm{p}}} \:=\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{2}^{\mathrm{3}\boldsymbol{\mathrm{p}}} \:=\:? \\ $$ Answered by A5T last updated on 15/Apr/24 $$\mathrm{2}^{\mathrm{2}{p}} =\mathrm{5}\Rightarrow\mathrm{2}^{\mathrm{3}{p}}…

if-f-x-x-x-2-then-f-1-x-

Question Number 206458 by mathlove last updated on 15/Apr/24 $${if}\:{f}\left({x}\right)=\sqrt{{x}−{x}^{\mathrm{2}} }\:\:\:\:\:{then}\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by Skabetix last updated on 15/Apr/24 $${f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{1}\pm\sqrt{−\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}} \\…