Question

if alpha and beta are complementary angles, sin alpha =3/5, then sin alpha cos beta - cos alpha sin beta​

Answer 1

Answer:

0

Step-by-step explanation:

Answer 2

The value of {(Sin α * Cos β) - (Cos α * Sin β)} is - 7/25.

Given,

α and β are complementary angles

Sin α = 3/5

To Find,

Sin α * Cos β - Cos α * Sin β

Solution,

It has been given that α and β are complementary angles

Thus, α + β = 90°

and, β = 90° - α

Sin α = 3/5

We can find Cos α by using the formula -

Sin²θ + Cos²θ = 1

(3/5)² + Cos²α = 1

Cos²α = 1 - (3/5)²

Cos²α = 1 - 9/25

Cos²α = (25 - 9)/25

Cos²α = 16/25

Cos α = √(16/25)

Cos α = 4/5

Also, Sin (90° - θ) = Cos θ

and Cos (90° - θ) = Sin θ

Sin α * Cos β - Cos α * Sin β

Sin α * Cos (90° - α) - Cos α * Sin (90° - α)

Sin α * Sin α - Cos α * Cos α

Sin²α - Cos²α

(3/5)² - (4/5)²

9/25 - 16/25

-7/25

Hence, the value of expression is -7/25.

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