In the following match each item given under the Column I to its correct answer given under the Column II.
`{:(,"Column I",,"Column II"),((i),sin(x+y)sin(x-y),(a),cos^(2)x-sin^(2)y),((ii),cos(x+y)cos(x-y),(b),1-tantheta//1+tantheta),((iii),cot((pi)/(4)+theta),(c),1+tantheta//1-tantheta),((iv),tan((pi)/(4)+theta),(d),sin^(2)x-sin^(2)y):}`

Explanation

(i) `sin(x+y)sin(x-y)=sin^(2)x-sin^(2)y`
(ii) `cos(x+y)cos(x-y)=cos^(2)x-sin^(2)y`
(iii) `cot((pi)/(4)+theta)=(cot""(pi)/(4)cottheta-1)/(cot""(pi)/(4)+cottheta)`
`" "=(-1+cottheta)/(1+cottheta)=(1-tantheta)/(1+tantheta)`
(iv) `tan((pi)/(4)+theta)=(tan""(pi)/(4)+tantheta)/(1-tan""(pi)/(4)tantheta)=(1+tantheta)/(1-tantheta)`
Hence, the correct mathes are `(i)to(d), (ii)to (a), (iii)to(b), (iv)to(c)`.