(sin^(2)20+sin^(2)70)/(cos^(2)20+cos^(2)70)+(sin(90-theta)sin theta)/(tan theta)+(cos(90-theta)cos theta)/(cos^(2)40+cos^(2)50)

Without using trigonometric tables,evaluate each of the following: (sin^(2)20^(@)+sin^(2)70^(@))/(cos^(2)20^(0)+cos^(2)70^(@))+(sin(90^(@)-theta)sin theta)/(tan theta)+(cos(90^(@)-theta)cos theta)/(cot theta)+cos(40^(0)+theta)-sin(50^(@)-theta)+(cos^(2)40^(0)+cos^(2)50^(@))/(sin^(2)40^(0)+sin^(2)50^(@))

Without using trigonometric tables, evaluate each of the following: (sin^2 20^0+sin^2 70^0)/(cos^2 20^0+cos^2 70^0)+(sin(90^0-theta)sintheta)/(tantheta)+(cos(90^0-theta)costheta)/(cottheta)

(sin^(2) 20^(@) + sin^(2) 70^(@))/(cos^(2) 20^(@) + cos^(2) 70^(@)) + [ (sin (90^(@) - theta).sin theta)/(tan theta) + (cos (90^(@) - theta).cos theta)/(cot theta) ] .

(sin theta+sin2 theta)/(1+cos theta+cos2 theta)=tan theta

(sin theta+sin2 theta)/(1+cos theta+cos2 theta)=tan theta

sin theta cos(90^(@)-theta)+cos theta sin(90^(@)-theta)

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

Simplify [(sin theta)/(cos theta)+(cos theta)/(sin theta)]^(2)

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)