If `cos A+ sin A=(1)/(2(cosA-sinA)),(0^(@) lt A lt 90^(@))`, then `sin^(2)A`=____________

If sin theta=(1)/(2) and 0^(@) lt theta lt 90^(@) , then cos2 theta =_________

If 2cos theta - sin theta = 1/sqrt(2), (0^(@) lt theta lt 90^(@)) then the value of 2sin theta + cos theta is:

In sin(A+B)=sqrt(3)/2 and cos(A-B)=1, 0 lt A + B lt 90^(@), A ge B .

If sin(A-B)=(1)/(2) and cos(A+B)=(1)/(2) , 0^(@) lt (A+B) lt 90^(@) and A gt B then find A and B .

In sin (A+B) =(sqrt(3))/(2) and cos (A-B)=1, 0 lt A +B lt 90^@ , A ge B.

If cos A =-3//5 , sin B=7//25 and 90^(@) lt A lt 180^@,0^(@) lt B lt 90^(@) , "then " tan (A+B)=

If tanA = 1(0^(@) lt A lt 90^(@)) and cos B = 1/sqrt(2) (0^(@) lt B lt 90^(@)) , then find cos(A + B)

If sin (A-B) =(1)/(2) ,cos (A+B) =(1)/(2) , where 0^@ lt A +B lt 90 ^(@) and A gt B find A and B

If sin 4 A - cos 2A = cos 4A - sin 2A, (0 lt A lt (pi)/(4)) then the value of tan 4A is

If sin theta = 12/13 (0^(@) lt theta lt 90^(@)) , find the value of (sin^(2) theta - cos^(2)theta)/(2 sin theta cos theta) xx (1)/(tan^(2)theta) .