What is `(sin5x-sin3x)/(cos5x+cos3x)` equal to ?

Options

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

Answer

C

Explanation

`(sin5x-sin3x)/(cos5x+cos3x)`
`sinc-sind=2cos((c+d)/(2))sin((c-d)/(2))`
`cos c-cosd=2((c+d)/(2))cos((c-d)/(2))`
`therefore(sin5x-sin3x)/(cos5x+cos3x)=(2cos((5x+3x)/(2))sin((5x-3x)/(2)))/(2cos((5x+3x)/(2))cos((5x-3x)/(2)))`
`=(sin((2x)/(2)))/(cos((2x)/(2)))=(sinx)/(cosx)=tanx`.