cos x = 4 / 5
sin x = ±√ ( 1 - sin^2 x )
The angles which lie between 0° and 90° are lie in the first quadrant.
In the first quadrant sin x is positive so:
sin x = √ ( 1 - sin^2 x )
sin x = √ ( 1 - sin^2 x ) = sin x = √ [ 1 - ( 4 / 5 ) ^ 2 ] =
√ [ 1 - 16 / 25 ] = √ [ 25 / 25 - 16 / 25 ] =
√ [ 9 / 25 ] = √ 9 / √ 25 = 3 / 5
sin x = 3 / 5
Now:
tan x = sin x / cos x
tan x = ( 3 / 5 ) / ( 4 / 5 ) = 3 * 5 / 4 * 5 = 3 / 4
tan x = 3 / 4
( 1 + tan x ) / ( 1 - tan x ) =
( 1 + 3 / 4 ) / ( 1 - 3 / 4 ) =
( 4 / 4 + 3 / 4 ) / ( 4 / 4 - 3 / 4 ) =
( 7 / 4 ) / ( 1 / 4 ) = 7 * 4 / 1 * 4 = 7 / 1 = 7
If cos x = 4/5, 0° x 90°, find the value
of (1 + tan x)/(1 - tan x)
2 answers
In QI, if cosx = 4/5, sinx = 3/5
(1+tanx)/(1-tanx) = (cosx+sinx)/(cosx-sinx)
= (4/5 + 3/5)/(4/5 - 3/5)
= (7/5)/(1/5)
= 7
(1+tanx)/(1-tanx) = (cosx+sinx)/(cosx-sinx)
= (4/5 + 3/5)/(4/5 - 3/5)
= (7/5)/(1/5)
= 7
1 answer