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Category: Algebra

if-sinx-2-3-then-find-you-the-value-of-sin-6-x-cos-6-x-

Question Number 196639 by bbbbbbbb last updated on 29/Aug/23 $$\mathrm{if}\:\mathrm{sinx}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{sin}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{cos}}^{\mathrm{6}} \boldsymbol{\mathrm{x}}??? \\ $$ Answered by AST last updated on 28/Aug/23 $$=\left({sin}^{\mathrm{2}} {x}+{cos}^{\mathrm{2}} {x}\right)^{\mathrm{3}} −\mathrm{3}{sin}^{\mathrm{2}}…

If-x-log-a-bc-y-log-b-ca-and-z-log-c-ab-then-prove-that-x-y-z-xyz-2-

Question Number 196582 by MATHEMATICSAM last updated on 27/Aug/23 $$\mathrm{If}\:{x}\:=\:\mathrm{log}_{{a}} {bc},\:{y}\:=\:\mathrm{log}_{{b}} {ca}\:\mathrm{and}\:{z}\:=\:\mathrm{log}_{{c}} {ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:{x}\:+\:{y}\:+\:{z}\:=\:{xyz}\:−\:\mathrm{2}. \\ $$ Answered by som(math1967) last updated on 27/Aug/23 $${x}={log}_{{a}}…