Simplify sec theta sin theta tan theta using basic identiti

Simplify: sec theta - sin theta tan theta using basic identities Sin A = 4/5 cos B = 5/13 Fin sin(A + B)

Solution

a) sec - sin*tan = (1/cos) - sin(sin/cos) = (1/cos)*[1 - sin^2 ] = (1/cos)*cos^2 = cos

b) sin A = 4/5

cosA = -3/5

cosB = 5/13

sinB = 12/13

sin(A + B) = sin A cos B + cos A sin B

= (4/5)*(5/13) + (-3/5)*(12/13) = 4/13 - 36/65 = -16/65