Identities, Please Help??

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Answer 1 · 2018-05-05T08:20:10

Please see the explanation below.

#"Question (a)"#

#arcsin(x^2-1)=1/3pi#

#sin(1/3pi)=x^2-1#

#x^2-1=sqrt3/2#

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

#x=+-sqrt((sqrt 3/2+1))=+-1.366#

#"Question (b)"#

#sin(2theta+1/3pi)=1/2#

#(2theta+1/3pi)=arcsin(1/2)#

#{(2theta+1/3pi=pi/6),(2theta+1/3pi=5/6pi), (2theta+1/3pi=13/6pi),(2theta+1/3pi=17/6pi):}#

#<=>#, #{(2theta=-1/3pi+pi/6=-1/3pi),(2theta=-1/3pi+5/6pi=pi/2), (2theta=-1/3pi+13/6pi=11/6pi),(2theta=-1/3pi+17/6pi=5/2pi):}#

#<=>#, #{(theta=-1/6pi),(theta=pi/4), (theta=11/12pi),(theta=5/4pi):}#

The solutions must be for #x in [0, pi]#

The solutions are

#S={pi/4, 11/12pi}#