Question

find the value of the expression:
(sum difference formulas)
cos(sin^-1(1/3)-tan^-1(1/2)

Answer 1

subtraction angle formula for cosine here

Answer 2

\[\cos(a-b)=\cos(a)\cos(b)-\sin(a)\sin(b)\] put \[a=\sin^{-1}(\frac{1}{3}),b=\tan^{-1}(\frac{1}{2})\]

Answer 3

oops i made a typo sorry

Answer 4

\[\cos(a-b)=\cos(a)\cos(b)\color{red}+\sin(a)\sin(b)\]

Answer 5

get \[=\cos(\sin^{-1}(\frac{1}{2}))\cos(\tan^{-1}(\frac{1}{2}))\color{red}+\sin(\sin^{-1}(\frac{1}{2}))\sin(\tan^{-1}(\frac{1}{2}))\]

Answer 6

of course you still have a pile of work to do