Question

If 3Tan theta = 4 , then ✓1-sin theta/1 + sin theta is equal to

Answer 1

heya..!!!!

here, alpha = ∅

3tan∅ = 4

=> tan∅ = 4/3 = perpendicular/base

perpendicular= 4 , base = 3

h² = 4² + 3²

=> h² = 25

=> h = 5

cos ∅ = 3/5 = p/h

=> 1/sec∅ = 3/5

=> sec∅ = 5/3

$\sqrt{ \frac{1 - sin \alpha }{1 + sin \alpha } } \times \frac{ \sqrt{1 - sin \alpha } }{ \sqrt{1 - sin \alpha } } \\ \\ = > \frac{1 - sin \alpha }{cos \alpha } \\ \\ = > sec \alpha - tan \alpha$

=> 5/3 - 4/3

=> (5-4)/3

=> 1/3

Answer 2

Hii friend,

Let theta = @

3 Tan@ = 4

Tan@ = 4/3

Under root 1 - Sin@ / 1 + Sin@ = ✓ 1-Sin@ / 1+Sin@ × 1-Sin@ / 1 - Sin@

= (1-Sin@)/ Cos@

= 1/Cos@ - Sin@/Cos@

= Sec@ - Tan@ [ 1/Cos@ = Sec@ and Sin@/Cos @ = Tan@]

= ✓ 1+ Tan²@ - Tan@

= ✓1 + (4/3)² - 4/3

= ✓1+16/9 - 4/3

= 5/3 -4/3

= 5-4÷3 = 1/3

HOPE IT WILL HELP YOU..... :-)