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)

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