cot theta =3/4 then sin theta -cos theta /sin theta +cos theta
Answers
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:
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