if log3 x²=2 then find x ?
Answers
Answer:
Correct Question :
sin x + sin 3x / cos x + cos 3x = tan 2x
Given :
sin x + sin 3x / cos x + cos 3x
To Prove :
sin x-sin 3x / cos x+cos 3x =tan 2x
Solution :
Using Identities :
sin x + sin y = 2sin x+y/2 cos x-y/2
cos x + cos y = 2cos x+y/2 cos x-y/2
\longmapsto\tt{\dfrac{2sin\:\dfrac{x+3x}{2}\:cos\:\dfrac{x-3x}{2}}{2cos\:\dfrac{x+3x}{2}\:cos\:\dfrac{x-3y}{2}}}⟼
2cos
2
x+3x
cos
2
x−3y
2sin
2
x+3x
cos
2
x−3x
\longmapsto\tt{\dfrac{2sin\:\dfrac{{\not{4x}}}{{\not{2}}}\:cos\:\dfrac{{\cancel{-2x}}}{{\not{2}}}}{2cos\:\dfrac{{\not{4x}}}{2}\:cos\:\dfrac{{\cancel{-2x}}}{{\not{2}}}}}⟼
2cos
2
4x
cos
2
−2x
2sin
2
4x
cos
2
−2x
\longmapsto\tt{\dfrac{{\not{2}}\:sin\:2x\:{\cancel{cos-x}}}{{\not{2}}\:cos\:2x\:{\cancel{cos-x}}}}⟼
2cos2x
cos−x
2sin2x
cos−x
\longmapsto\tt{\dfrac{sin\:2x}{cos\:2x}}⟼
cos2x
sin2x
tan2x