Question

if 0 < A < pi /4 and cosA = 4/5 then find the value of sin2A and cos2A
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Answer 1

Here is your answer

Hope you understand it

Answer 2

The values of Sin 2A and Cos 2A are 24/25 and 7/25 respectively.

Given,

A ∈ (0, π/4)

Cos A = 4/5

To Find,

Sin 2A and Cos 2A

Solution,

Since A ∈ (0, π/4), then 2A ∈ (0, π/2)

Cos A = 4/5

Sin²A + Cos²A = 1

Sin²A + (4/5)² = 1

Sin²A + 16/25 = 1

Sin²A = 1 - 16/25

Sin²A = 9/25

Sin A = √(9/25)

Sin A = 3/5

Now using the double angle formula we can get,

Sin 2A = 2*Sin A*Cos A

Sin 2A = 2*(3/5)*(4/5)

Sin 2A = 24/25

Cos 2A = Cos²A - Sin²A

Cos 2A = (4/5)² - (3/5)²

Cos 2A = 16/25 - 9/25

Cos 2A = 7/25

Hence the values of Sin 2A and Cos 2A are 24/25 and 7/25 respectively.

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