Question

sin x + cos x=

$\sqrt{2}$
sin 5x.​

Answer 1

Answer:

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Step-by-step explanation:

LHS

cos5x−cosx

sin5x+sinx−2sin3x

​  

 

=  

2sin(  

2

5x+x

​  

)sin(  

2

x−5x

​  

)

2sin(  

2

5x+x

​  

)cos(  

2

5x−x

​  

)−2sin3x

​  

 

=  

2sin3xsin(−2x)

2sin3xcos2x−2sin3x

​  

∴sin(−θ)=−sinθ

=  

−2sin3xsin2x

2sin3x(cos2x−1)

​  

 

=  

sin2x

1−cos2x

​  

 

=  

2sinxcosx

1−(1−2sin  

2

x)

​  

 

=  

2sinxcosx

1−1+2sin  

2

x

​  

 

=  

2sinxcosx

2sin  

2

x

​  

 

=  

cosx

sinx

​  

 

=tanxRHS