costan1512 cos145Solutiongiven cos tan1512 cos145 costan

Solution

given

cos( tan^-1(5/12) + cos^-1(4/5) ) = cos(tan^-1(5/12))*cos(cos^-1(4/5)) - sin(tan^-1(5/12))*sin(cos^-1(4/5))

= cos(cos^-1(12/13))*(4/5) - sin(sin^-1(5/13))*sin(sin^-1(3/5))

= 12/13*4/5 - 5/13*3/5

= 48/65 - 15/65

= 33/65

use

cos (A + B) = (cos A)cos B - (sin A)sin B

for a 4-3-5 triangle ___ tan^-1 (3/4) = cos^-1 (4/5) = sin^-1 (3/5)

for a 5-12-13 triangle ___ cos^-1 (12/13) = sin^-1 (5/13)