Question #5e3fc

1 Answer
Jan 8, 2018

See below.

Explanation:

#LHS#

Identity:

#color(red)(sin(A+B)=sinAcosB+cosAsinB)#

#sin(3x)=sin(x+2x)=sin(x)cos(2x)+cos(x)sin(2x)#

#(sin(x)cos(2x)+cos(x)sin(2x))/(sinxcosx)=>#

#(sin(x)cos(2x))/(sin(x)cos(x))+(cos(x)sin(2x))/(sin(x)cos(x))#

#(cancel(sin(x))cos(2x))/(cancel(sin(x))cos(x))+(cancel(cos(x))sin(2x))/(sin(x)cancel(cos(x)))#

#cos(2x)/cos(x)+sin(2x)/sin(x)#

Identities:

#color(red)(sin(2A)=2sin(A)cos(A))#

#color(red)(cos(2A)=2cos^2(A)-1)#

#(2cos^2(x)-1)/cos(x)+(2sin(x)cos(x))/sin(x)#

#2cos(x)-1/cos(x)+2cos(x)=4cos(x)-1/cos(x)#

Identity

#color(red)(1/cos(A)=sec(A))#

#->=4cos(x)-sec(x)#

#LHS-=RHS#