NEED ASAP!! use right triangles to find the exact value of

Question

cos [tan^-1( 4/3) + cos^-1 ( 5/13 ) ]

cos [tan ^-1 (4 over 3) + cos ^-1 (5 over 13)]

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Answer 1

Use the sum of two angles formula cos(x+y) = cosx cosy - sinx siny

so it is same as cos(tan^-1 4/3) cos(cos^-15/13) - sin(tan^-14/3) sin(cos^-15/13)

now use the right triangle definitions of trigs to find the values

cos(tan^-1 4/3)=3/5, cos(cos^-15/13)=5/13, sin(tan^-14/3)=4/5, sin(cos^-15/13)=12/13

so 3/5 times 5/13 - 4/5 times 12/13 = 3/13 - 36/169 = 3/169