Question

Sin5x-2sin3x+sinx/cos5x-cosx

Answer 1

Answer:

here is your answer:

Step-by-step explanation:

Formula:

sinC−sinD=2cos(  

2

C+D

​

)sin(  

2

C−D

​

)

cosC−cosD=−2sin(  

2

C+D

​

)sin(  

2

C−D

​

)

LHS=  

cos5x−cosx

sin5x−2sin3x+sinx

​

 

=  

cos5x−cosx

(sin5x−sin3x)−(sin3x−sinx)

​

 

=  

−2sin3xsin2x

2cos4xsinx−2cos2xsinx

​

 

=  

−2sin3xsin2x

2sinx(cos4x−cos2x)

​

 

=  

−2sin3x(2sinxcosx)

2sinx(−2sin3xsinx)

​

 

=  

cosx

sinx

​

 

=tanx=RHS

LHS=RHS