If `tan theta=sqrt2-1` then `sin theta cos theta=`

If sin theta=1/sqrt2 then tan theta+cos theta=

If tan theta= (sqrt 2)-1 ,prove that sin theta cos theta = 1/2 . .

If cos theta+sin theta=sqrt2 cos theta, show that cos theta-sin theta=sqrt2 sin theta .

If (sin theta + cos theta)/(sin theta - cos theta) = (5)/(4) , the value of (tan^(2) theta + 1)/(tan^(2) theta - 1) is

(xv) (cos^2 theta) / (1- tan theta) +( sin^3 theta)/ (sin theta - cos theta) = 1 + sin theta cos theta

Prove that (sin theta+cos theta)/(sin theta- cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = ( 2sec^(2) theta)/(tan^(2) theta -1) .

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

Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan theta, 1]]^(-1)=[[cos 2 theta, -sin 2 theta],[ sin 2 theta, cos 2 theta]]