Sin alpha betacos alpha cos beta tan alpha tan betaSoluti

Sin (alpha + beta)/cos (alpha) cos (beta) = tan (alpha) + tan (beta)

Solution

10.

Sin(a +b )/(cos(a)*cos(b)) = tan(a) + tan(b)

take LHS   

( sin(a) * cos(b) + cos(a)*sin(b) ) / ( cos(a)*cos(b) )

= ( sin(a) * cos(b) / ( cos(a)*cos(b) )  + cos(a)*sin(b) / ( cos(a)*cos(b) )

= sin(a) /cos(a) + sin(b) /cos(b)

= tan(a) + cos(b) = RHS

==>> LHS = RHS