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which of the following is equivalent to the expression sin 2x cos x-sin x cos2x 

 

a. sinx

b. sin 3x

c. cos x

d. cos 3x

 Nov 19, 2020

Best Answer 

 #1
avatar+11086 
+2

which of the following is equivalent to the expression sin 2x cos x-sin x cos2x 

a. sinx

b. sin 3x

c. cos x

d. cos 3x

 

Hello Debnath!

 

\(sin 2x\ cos x-sin x\ cos2x\\ = 2\ sinx\ cosx\ cosx-sinx\ (cos^2x-sin^2x)\\ =2sinx\ cos^2x-sinx\ cos^2x+sin^3x\\ =sinx\ cos^2x+sin^3x\\ =sinx(cos^2x+sin^2x)\\ =sinx\ \cdot 1\)

 

\(sin 2x\ cos x-sin x\ cos2x=sinx\)

laugh  !

 Nov 19, 2020
 #1
avatar+11086 
+2
Best Answer

which of the following is equivalent to the expression sin 2x cos x-sin x cos2x 

a. sinx

b. sin 3x

c. cos x

d. cos 3x

 

Hello Debnath!

 

\(sin 2x\ cos x-sin x\ cos2x\\ = 2\ sinx\ cosx\ cosx-sinx\ (cos^2x-sin^2x)\\ =2sinx\ cos^2x-sinx\ cos^2x+sin^3x\\ =sinx\ cos^2x+sin^3x\\ =sinx(cos^2x+sin^2x)\\ =sinx\ \cdot 1\)

 

\(sin 2x\ cos x-sin x\ cos2x=sinx\)

laugh  !

asinus Nov 19, 2020
 #2
avatar+38 
+1

thank you 

Debnath  Nov 19, 2020

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