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Learn Miscellaneous Exercise 3

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

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...
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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

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It is known that . L.H.S. = = tan 6x = R.H.S.
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It is known that

.

L.H.S. =

= tan 6x

= R.H.S.

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Comments

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