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Asked by Aarti Last Modified
Answer 
numerator=(sin7x+sin5x)+(sin9x+sin3x)
=2sin(12x/2)cos(2x/2)+2sin(12x/2)cos(6x/2) (sinA+sinB=2sin(A+B)/2 cos(A-B)/2 )
=2sin6x cosx+2sin6x cos3x
=2sin6x(cosx+cos3x)
=2sin6x(2cos(4x/2)cos(2x/2)) (cosA+cosB=2cos(A+B)/2 cos(A-B)/2)
=4sin6x cos2x cosx
denominator=(cos7x + cos5x)+(cos9x+cos3x) (cosA+cosB=2cos(A+B)/2 cos(A-B)/2)
=2cos(12x/2)cos(2x/2)+2cOs(12X/2)Cos(6X/2)
=2cos6x cosx +2cos6x cos3x
=2cos6x(cosx+cos3x)
=2cos6x * 2cos(4x/2)cos(2x/2)
=4cos6x cos2x cosx
LHS=(4sin6x cos2x cosx)/(4cos6x cos2x cosx)
=sin6x/cos6x
=tan6x
read lessIt is known that
.
L.H.S. = 
= tan 6x
= R.H.S.
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