Question

How is this solved using trig identities (sum/difference)?

Answer 1

The angle sum identity for cosine is:


`cos( \theta+ \beta) = cos( \theta)cos( \beta) - sin( \theta)sin( \beta)`

So we need to figure out the values of \theta and \beta.


`tan^(-1)( (1)/(2)) = \theta`


`cos^(-1)( (2)/(3) ) = \beta`


`cos(tan^(-1)( (1)/(2)))cos(cos^(-1)((2)/(3))) - sin(tan^(-1)( (1)/(2)))sin(cos^(-1)((2)/(3))) =` 0.26295 rad