`sin(40+theta).cos(10+theta)-cos(40+theta)sin(10+theta)=1/2`

(sin theta)/(1-cos theta)=(1+cos theta)/(sin theta)

Prove that (1)/(2){(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)}=(1)/(sin theta)

" 4."(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)=(2)/(sin theta)

(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)=2cos ec theta

(sin3 theta+cos3 theta)/(cos theta-sin theta)=1+2xx sin2 theta

Prove that :(sin theta cos(90^(0)-theta)cos theta)/(sin(90^(0)-theta))+(cos theta sin(90^(0)-theta)sin theta)/(cos(90^(@)-theta))=1csc^(2)(90^(@)-theta)-tan^(2)theta=cos^(2)(90^(@)-theta)+cos^(2)theta

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^(@))

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

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta

cos theta/(1+sin theta)=(1-sin theta)/cos theta