Question

If sinx =1/2 then find 1-tanx/1+tanx.

Answer 1

Step-by-step explanation:

$\frac{1 - \tan(x) }{1 + \tan(x ) } \\ \\ \frac{1 - \frac{ \sin(x) }{ \cos(x) } }{1 + \frac{ \sin(x) }{ \cos(x) } } \\ \\ \frac{? \cos(x - \sin(x) ) }{ \cos(x) } \div \frac{ \cos(x + \sin(x) ) }{ \cos(x) } \\ \\ \frac{1}{ \cos} \times \frac{ \cos}{1} \\ \\ = 1$

Answer 2

Since sin x = 1/2 -> x = 30°....

so tan x = 1/√3 (tan 30° = 1/√3)

-> (1 - 1/√3) / (1 + 1/√3)

-> (√3 - 1 /√3) / (√3 + 1/√3)            LCM

-> (√3-1 / √3) * (√3 /√3 + 1)

-> √3 - 1 / √3 + 1

Rationalise the denominator.

(√3 - 1 / √3 + 1) * (√3 - 1 / √3 - 1)

(√3-1)² / 3-1

(3- 2√3 + 1) / 2

4 -2√3 / 2

4/2 - 2√3/ 2

= 2 -√3