Posted by **Hannah** on Monday, May 6, 2013 at 10:10pm.

cos[(tan^-1(3/4))+(cos^-1(9/41))]

- Trig -
**Reiny**, Monday, May 6, 2013 at 10:42pm
let tan^-1 (3/4) = A and let cos^-1 (9/41) = B

then cos[(tan^-1(3/4))+(cos^-1(9/41))]

= cos(A + B)

= cosA cosB - sinA sinB

IF tan^-1 (3/4) = A

then tanA = 3/4

---> sinA = 3/5 and cosA = 4/5, recognize the 3-4-5 right angled triangle

if cos^-1 (9/41) = B

then cosB = 9/41

---> x^2 + y^2 = r^2

81 + y^2 = 1681

y^2 = 1600

y = √1600 = 40 and thus sinB = 40/41

so back to

cosA cosB - sinA sinB

= (4/5)(9/41) - (3/5)(40/41) = -84/205

( I tested my answer with my calculator, it is correct)

## Answer This Question

## Related Questions

- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Trig. - sec^2xcotx-cotx=tanx (1/cos)^2 times (1/tan)-(1/tan)=tan (1/cos^2) times...
- trig - Show that 1-cos2A/Cos^2*A = tan^2*A 1-cos2A/Cos^2*A = [Cos^2(A) - Cos(2A...
- precalculus - For each of the following determine whether or not it is an ...
- trig 26 - simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v ...
- TRIG - what is another form of: sin (A+B) sin (A-B)/ cos^2 A cos^2 B a) cos^2 A...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Trigonometry desperate help, clueless girl here - 2. solve cos 2x-3sin x cos 2x...
- Trigonometry - Please review and tell me if i did something wrong. Find the ...

More Related Questions