(COS3A +COSA)/(SIN3A-SINA) +(COS2A-COS4A)/(SIN4A-SIN2A) = SIN A .SEC A . SEC3A
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LHS
(cos3A+cosA)/(sin3A-sinA)+(cos2A-cos4A)/(sin4A-sin2A)
=(2cos2AcosA/2cos2AsinA)+(2sin3AsinA/2cos3AsinA)
=cosA/sinA+sin3A/cos3A
=(cos3AcosA+sin3AsinA)/sinAcos3A
=cos(3A-A)/sinAcos3A
=cos2A/sinAcos3A
RHS
sinAsecAsec3A
=sinA/cosAcos3A
Here, LHS≠RHS
The given problem is wrong.
(cos3A+cosA)/(sin3A-sinA)+(cos2A-cos4A)/(sin4A-sin2A)
=(2cos2AcosA/2cos2AsinA)+(2sin3AsinA/2cos3AsinA)
=cosA/sinA+sin3A/cos3A
=(cos3AcosA+sin3AsinA)/sinAcos3A
=cos(3A-A)/sinAcos3A
=cos2A/sinAcos3A
RHS
sinAsecAsec3A
=sinA/cosAcos3A
Here, LHS≠RHS
The given problem is wrong.
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