Give the exact value of the expression without using a calcu

Give the exact value of the expression without using a calculator. cos (tan^-1 8/15 + tan^-1 (-12/5)) cos (tan^-1 8/15 + tan^-1 (-12/5)) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

cos(tan^-1(8/15) + tan^-1(-12/5)) = cos(tan^-1[(8/15 -12/5)/(1 - (8/15)(-12/5))])

= cos(tan^-1[-140/171])

= cos(-39.30765^o) = 0.773755656