`cos^2((pi)/(4)-theta)+cos^2((pi)/(4)+theta)=.....`

Prove that: cos^(2)((pi)/(4)-theta)-sin^(2)((pi)/(4)-theta)=s in2 theta

The maximum value of 1+sin((pi)/(4) +theta) +2cos((pi)/(4) - theta) for all real values of theta is :

Prove that cos ec((pi)/(4)+(theta)/(2))cos ec((pi)/(4)-(theta)/(2))=2sec theta

Cos^(2)(pi/4-theta/2)-sin^(2)(pi/4-theta/2)=

I : If sin((pi)/(4)cot theta)=cos ((pi)/(4)tan theta) then theta = n pi+pi//4, n in Z II : If tan ((pi)/(2)sin theta)=cot((pi)/(2)cos theta) then sin (theta + (pi)/(4))= pm (1)/(sqrt(2))

If cos^(3) theta + cos^(3)((2pi)/(3) + theta) + cos^(3)((4pi)/(3) + theta) = a cos 3 theta , then a =

The maximum value of 1+sin((pi)/(4)+theta)+2cos((pi)/(4)-theta) for real values of theta is

The maximum value of 1+sin((pi)/(4)+theta)+2cos((pi)/(4)-theta) for real values of theta is