Question

Given 4 sin theta = 3 cos theta , find the value of :
(i). Sin theta
(ii). Cos theta
(iii). Cot^2 theta - cosec^2 theta

Answer 1

Answer:sin(they)=3/5

Cos(they)=4/5

iii> -1

Step-by-step explanation:

Answer 2

AnswEr :

Given : 4 sin(θ) = 3 cos(θ)

To Find :

1. Sin(θ)
2. Cos(θ)
3. Cot²(θ) - Cosec²(θ)

⋆ so, we have given identity is -

⇝ 4 sin(θ) = 3 cos(θ)

⇝ sin(θ) / cos(θ) = 3 / 4

⇝ tan(θ) = 3 / 4 = p / b

⠀⠀✡ p = 3 and, b = 4

⋆ we can find out h with Pythagoras -

⇝ h² = p² + h²

⇝ h² = ( 3 )² + ( 4 )²

⇝ h² = ( 9 + 16 )

⇝ h² = 25

⇝ h = √25

⇝ h = 5

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1) Sin(θ)

⇒ Sin(θ) = p / h

• Using the Values

⇒ Sin(θ) = 3 / 5

2) Cos(θ)

⇒ Cos(θ) = b / h

• Using the Values

⇒ Cos(θ) = 4 / 5

3) Cot²(θ) - Cosec²(θ)

⇒ Cot²(θ) - Cosec²(θ) = (b / p)² - (h / p)²

⇒ Cot²(θ) - Cosec²(θ) = (4 / 3)² - (5 / 3)²

⇒ Cot²(θ) - Cosec²(θ) = (16 / 9) - (25 / 9)

⇒ Cot²(θ) - Cosec²(θ) = ( 16 - 25 ) / 9

⇒ Cot²(θ) - Cosec²(θ) = - 9 / 9

⇒ Cot²(θ) - Cosec²(θ) = - 1

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⋆ Some Information Related to this :

⇀ Sin(θ) = Perpendicular/Height = 1/Csc(θ)

⇁ Cos(θ) = Base/Height = 1/Sec(θ)

⇀ Tan(θ) = Perpendicular/Base = 1/Cot(θ)

⇁ Sin²(θ) + Cos²(θ) = 1

⇀ Sec²(θ) - Tan²(θ) = 1

⇁ Cosec²(θ) - Cot²(θ) = 1