Question

If tan theta is equal to 5/4, find sin square theta minus cos square theta

Answer 1

Answer:

9/41

explanation-

tan θ = opposite/adjacent =5/4

hypotenuse = √(4²+5²)

= √(41)

so, cos θ = adjacent / hypotenuse = 4/√(41)

sin θ = opposite / hypotenuse = 5/√(41)

therefore,

sin²θ - cos²θ = (5/√(41))² - (4/√(41))²

= (25/41) - (16/41)

= 9/41

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