What is the value of sin 7x ndash sin 5x divide cos 7x cos 5x ndash cos 6x ndash cos 4x divide sin 6...........

Quantitative Aptitude (CGL) Mensuration 3D

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What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

2 tan x

tan 2 x

tan (3 x/2)

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Explanation:

Step-by-step explanation:
[(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]
sinA+sinB=2sin(A+B/2).cos(A+B/2)
sinA-sinB=2cos(A+B/2).sin(A+B/2)
cosA+cosB=2cos(A+B/2).cos(A-B/2)
cosA-cosB= -2sin(A+B/2).sin(A-B/2)
now,
sin7x-sin5x = 2cos6x.sinx
cos7x+cos5x = 2cos6x.cosx
cos6x-cos4x = -2sin5x.sinx
sin6x+sin4x = 2sin5x.cosx
putting these values in the given problem, we get,
((2cos6x.sinx)÷(2cos6x.cosx))-((-2sin5x.sinx)÷(2sin5x.cosx))
sinx/cosx + sinx/cosx
tanx + tanx
2tanx