trig exercise of sums and differences identities

Question

If cosα=0.891 and cosβ=0.577 with both angles’ terminal rays in Quadrant-I, find the values of tan(α+β)
Your answers should be accurate to 4 decimal places.

please help, thanks!

Answer 1

tan(α+β)=(tan(α)+tan(β))/(1+tan(α)tan(β)) (*)

If we know cos(α) (and cos(β)) then we can find tan(α)  ( and tan(β) ) as

tan(α)=√(1/cos^2(α)-1)=√(1/(0.891)^2 -1)=

The same with

tan(β)=√(1/cos^2(β)-1)=√(1/(0.577)^2 -1)=

Caculate tan(α) and tan(β) and plug in into (*).