as29006
Calculators
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
as29006
as29006
Home
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
MATH SOLVE
Home
General
Find all solutions to the equation (sinx-cosx)^2=3
4 months ago
Q:
Find all solutions to the equation (sinx-cosx)^2=3
Accepted Solution
A:
Answer:no solutionsStep-by-step explanation:Simplify the equation [tex](\sin x-\cos x)^2=3:[/tex][tex]\sin^2 x-2\sin x\cos x+\cos ^2x=3,\\ \\ (\sin^2x+\cos^2x)-2\sin x\cos x=3.\\[/tex]Since [tex]\sin^2 x+\cos^2 x=1[/tex]and [tex]2\sin x\cos x=\sin 2x,[/tex]we have[tex]1-\sin 2x=3,\\ \\\sin 2x=-2.[/tex]Since [tex]\sin 2x[/tex] cannot be less than [tex]-1,[/tex] this equation has no solutions.