`(sin 5x-sin 3x)/(cos 5x + cos 3x)` किसके बराबर है ?

Options

A. `sin x`
B. `cos x`
C. `tan x`
D. `cot x`

Answer

C

Explanation

दिया है,
`(sin 5x-sin 3x)/(sin 5x+sin 3x)`
`=(2cos((5x+3x)/(2))sin((5x-3x)/(2)))/(2cos((5x+3x)/(2))cos((5x-3x)/(2))) " " [:'sinC-sin D = 2 cos ((C+D)/(2))sin((C-D)/(2)) " तथा " cos C + cos D = 2 cos ((C+D)/(2))cos((C-D)/(2))]`
`=(2cos 4x sin x)/(2cos 4x cos x)`
`=(sin x)/(cos x)`
`= tan x`