The value of `(2sinx)/(sin3x)+(tanx)/(tan3x)` is________.

Answer

1

Explanation

` ( 2sin x )/(sin 3x) + ( tan x)/(tan 3x) = ( 2 sin x )/( sinx*( 3-4 sin^(2)x)) + (tan x)/(((3tan x - tan^(3)x))/((1-3 tan ^(2) x)))`
`" " = (2)/( 3-4 sin^(2) x ) + ((1-3 tan ^(2)x))/(( 3 - tan ^(2)x))`
`" " = (2)/(3-4sin^(2)x ) + (1-((3sin^(2)x)/(1-sin^(2)x)))/(3-((sin^(2)x)/(1-sin^(2)x)))`
`" " = (2)/(3-4 sin^(2)x )+ ((1-4 sin^(2) x))/( 3-4 sin^(2)x))`
`" " ((3-4 sin ^(2)x))/((3-4 sin ^(2)x)) = 1`