Prove that`sin^2(pi/4-x)+sin^2(pi/4+x)=1`

Prove that sin^2(pi/8)+sin^2(3pi/8)+sin^2(5pi/8)+sin^2(7pi/8)=2

Prove that: sin^(2) (pi/8) +sin^(2) ((3pi)/8) +sin^(2)((5pi)/8)+sin^(2)((7pi)/8)=2

Solve the following:Show that sin^2(pi/10)+sin^2((4pi)/10)+sin^2 ((6pi)/10)+sin^2 ((9pi)/10)=2

1-2sin^2(pi/4+theta)=

Prove the following: cos(pi/4-x).cos(pi/4-y)-sin(pi/4-x).sin(pi/4-y)=sin(x+y)

Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

Prove that (i) " cos " ((pi)/(4) + x) + " cos " ((pi)/(4)- x) =sqrt(2) " cos " x (ii) " cos " ((3pi)/(4) + x) - "cos " ((3pi)/(4)-x) =- sqrt(2) " sin " x

Using derivative prove that sin^(-1) x + cos^(-1) x = (pi)/2

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

Prove the following: cos(pi/4+x)+cos(pi/4-x)=sqrt2cosx