Question

If tantheta = 12/5, then find the value of 1+sintheta/1-sintheta​

Answer 1

Topic : Trigonometry

Given : tan∅ = 12/5

To Find : ( 1 + sin∅ ) / ( 1 - sin∅ )

Solution :

tan∅ = Perpendicular / Base

Perpendicular / Base = 12/5

We can assume that,

• Perpendicular = 12x

• Base = 5x

Applying Pythagoras Theorem,

( Hypotenuse )² = ( Perpendicular )² + ( Base )²

( Hypotenuse )² = ( 12x )² + ( 5x )²

( Hypotenuse )² = 144x² + 25x²

( Hypotenuse )² = 169x²

( Hypotenuse )² = (13x)²

Hypotenuse = 13x

Value of sin∅,

sin∅ = Perpendicular/Hypotenuse

sin∅ = 12x / 13x

sin∅ = 12/13

Solving for required value,

( 1 + sin∅ ) / ( 1 - sin∅ )

Replace sin∅ with 12/13,

( 1 + (12/13) ) / ( 1 - (12/13) )

((13 + 12)/13) / ((13 - 12)/13)

(25/13) / (1/13)

13 gets cancelled out,so

25

Answer : Required value is 25.