Write the trigonometric expression as an algebraic expression.

Question

sin(arctan(2x) − arccos(x))

= ________

Answer 1

sin(arctan(2x) - arccos(x)); Let α = arctan(2x) and β = arccos(x).

Then we have: sin(α - β) = sinαcosβ - cosαsinβ;

tanα = 2x; cosβ = x; sinβ = √1 - x²;

cosα = 1/√1 + 4x²; sinα = 2x/√1 + 4x²;

sin(arctan(2x) - arccos(x)) = 2x²/√1 + 4x² - √1 - x²/√1 + 4x² (2x² - √1 - x²)/√1 + 4x²