show that the point P(aSectheta,bTantheta) lies on the hyperbola x2/a2_y2/b2=1 and find the equation of tangent and normal at theta

Hint: as is often the case when dealing with functions like secant and tangent, it's helpful to replace them with their sine and cosine equivalents, then look for common identites that you can apply, such as \sin^2 \theta + \cos^2 \theta = 1.