Question

cot theta =3/4 then sin theta -cos theta /sin theta +cos theta​

Answer 1

Answer:

1/7.

Step-by-step explanation:

cot theta = Base/Perpendicular = 3/4.

By Using Pythagoras Theorem,

Hypotenuse² = 3² + 4²

Hypotenuse = √9+16 = √25 = 5.

sin theta = Perpendicular/Hypotenuse = 4/5.

cos theta = Base/Hypotenuse = 3/5.

Therefore, sin theta -cos theta /sin theta +cos theta​ =

4/5-3/5 ÷ 4/5+3/5.

1/5 ÷ 7/5 = 1/5*5/7 = 1/7.

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Answer 2

Answer:

Step-by-step explanation:

Let the triangle be ABC, right angles at B.

And ∠A = θ.

cot θ = 3/4

BA/BC = 3/4

⇒BA = 3x                AND                 BC = 4x                      , x is a real number

AC^2 = BA^2 + BC^2

         = (3x)^2 + (4x)^2

         = 9x^2 + 16x^2

         = 25x^2

AC = √(25x^2)

     = 5x

(sin θ - cos θ)/(sin θ + cos θ) = (4x/5x - 3x/5x)/(4x/5x + 3x/5x)

                                               = (4/5 - 3/5)/(4/5 + 3/5)

                                               = (1/5)/(7/5)

                                               = 1/7