Question

show that sin 3theta=sin theta(2 cos 2theta +1)​

Answer 1

Step-by-step explanation:

dear reader,

sin 3 theota= sin theota (2cos 2theota+1)

Take sin theota on the left hand side

sin 3 theota/sin theota =(2 cos 2 theota +1)

L.H.S

sin3 theota /sin theota

= (3sin theota-4 sin^3 theota)/sin theota

= (3sin theota/sin theota )-(4sin^3 theota/sin theota)

=3-4sin^2 theota

=3-4(1-cos^2 theota)

=3-4+4 cos^2 theota

= -1+2(2cos^2 theota)

= -1+2(cos 2 theota+1)

= -1+2 cos 2 theota +2

=2cos2 theota+1

=RHS

hence proved

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