Question #98d02

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Answer 1 · 2016-03-28T22:16:46

The given equality is not an identity.

Take #x = pi/4#:

Left Hand Side# = sin^2(pi/4)+4sin(pi/4)+3/cos^2(pi/4)#

#= (sqrt(2)/2)^2+4(sqrt(2)/2)+3/(sqrt(2)/2)^2#

#=1/2 + 2sqrt(2) + 6#

#= 13/2+2sqrt(2)#

Right Hand Side# = sin(pi/4)+3/(1-sin(pi/4))#

#=sqrt(2)/2 + 3/(1-sqrt(2)/2)#

#=sqrt(2)/2 + (3(1+sqrt(2)/2))/(1/2)#

#=sqrt(2)/2 + (12+6sqrt(2))/2#

#=6+7/2sqrt(2)#

As the let hand side does not equal the right hand side at #x=pi/4#, the given equality is not an identity.