Homework SourseEvaluate the following without using a calculator Give exact
Evaluate the following without using a calculator. Give exact values.
cos[sin^-1(3/5)+cos^-1(5/13)]
Solution
cos[sin-1(3/5)+cos-1(5/13)]
cos(A+B)=cosAcosB -sinAsinB
=cos[sin-1(3/5)]cos[cos-1(5/13)] -sin[sin-1(3/5)]sin[cos-1(5/13)]
=cos[cos-1(4/5)]cos[cos-1(5/13)] -sin[sin-1(3/5)]sin[sin-1(12/13)]
=(4/5)(5/13) -(3/5)(12/13)
=(20/65)-(36/65)
=-16/65
![Evaluate the following without using a calculator. Give exact values. cos[sin^-1(3/5)+cos^-1(5/13)]Solutioncos[sin-1(3/5)+cos-1(5/13)] cos(A+B)=cosAcosB -sinAsi](/WebImages/20/evaluate-the-following-without-using-a-calculator-give-exact-1043447-1761542430-0.webp "Evaluate the following without using a calculator. Give exact values. cos[sin^-1(3/5)+cos^-1(5/13)]Solutioncos[sin-1(3/5)+cos-1(5/13)] cos(A+B)=cosAcosB -sinAsi")
