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

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

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

If sin theta+cos theta=1 then sin theta cos theta=

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

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

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

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

The value of ((sin theta -cos theta )(1+tan theta + cot theta ))/(1+sin theta cos theta ) = ?

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)