Posted by **AwesomeGuy** on Thursday, February 21, 2013 at 11:03pm.

Write the trigonometric expression as an algebraic expression.

1.) SIN(ARCSIN X+ARCCOS X)

ANSWER: 1

2.) SIN(ARCTAN 2X-ARCCOS X)

ANSWER: 2x²-SquareRoot of 1-x²/Square

Root of 4x²+1.

- Trigonometry -
**AwesomeGuy**, Thursday, February 21, 2013 at 11:18pm
1.) Apply the following method you used in #2! You should notably understand this already! Goodness grief!

2.) let A = arctan x

let B = arccos x

then we are looking for

sin(A + B) .

now,

tan A = x ,

sin A = x/√(x^2+1)

cos A = 1/√(x^2+1) ... create a right triangle where the opposite side is x, and the adjacent side is 1 ... the hypotenuse is √(x^2+1)

cos B = x

sin B = √(1 - x^2)

meanwhile

sin(A + B)

= sin A cos B + cos A sin B

= x/√(x^2+1) * x + 1/√(x^2+1) * √(1 - x^2)

= [x^2 + √(1 - x^2)] / (x^2 + 1) .

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