tan5A-tan3A/tan5A+tan3A=Sin2A / Sin8A
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Prove:
tan5A+tan3A
tan5A−tan3A
=
sin8A
sin2A
Answer
L.H.S
=
tan5A+tan3A
tan5A−tan3A
=
cos5A
sin5A
+
cos3A
sin3A
cos5A
sin5A
−
cos3A
sin3A
=
sin5A cos3A+sin3Acos5A
sin5Acos3A−sin3Acos5A
We know that
sin(A+B)=sinAcosB+cosAsinB
sin(A−B)=sinAcosB−cosAsinB
Therefore,
=
sin(5A+3A)
sin(5A−3A)
=
sin8A
sin2A
R.H.S
Hence, proved.
please
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