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) .

## Answer this Question

## Related Questions

- math - Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4. ...
- maths - Please can you help me with this question? Choose the option which is a ...
- math - Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4...
- Precal - Use a calculator to evaluate the expression. arcsin 0.45 arctan 15 ...
- Trigonometry - I need help with I just can't seem to get anywhere. this is as ...
- TRIGONOMETRY - Write the following trigonometric expression as an algebraic ...
- math - Eliminate the parameter (What does that mean?) and write a rectangular ...
- math - Can anyone help w/ these. 1) Solve the equation in the internal [0deg, ...
- Calculus - Book works out integral of sqtr(a^2-x^2)dx as a^2/2*arcsin(x/a)+x/2*...
- Trigonometry help - If sin(x) = 1/3 and sec(y) = 13/12 , where x and y lie ...