Evaluate the following: `sin(7pi)/(12)cospi/4-cos(7pi)/(12)sinpi/4`

Evaluate the following: (sin(7 pi))/(12)(cos pi)/(4)-(cos(7 pi))/(12)(sin pi)/(4)

sin((7pi)/(12))cos(pi/4)-cos((7pi)/(12))sin(pi/4)=...........

Evaluate : 1/2 - sin ^(2) ""(7pi)/(12)

Evaluate each of the following: sin^(-1)(sin(2pi)/3) (ii) cos^(-1)(cos(7pi)/6) (iii) tan^(-1)(tan(3pi)/4)

Prove any of the following: sin^2(pi/4)+sin^2(3pi/4)+sin^2(5pi/4)+sin^2(7pi/4)=2

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

(sin((5pi)/12)-cos((5pi)/12))/(cos((5pi)/12)+sin((5pi)/12))=

Prove the following : cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8) =3/2

Using application of trignometric formulas prove that (i)cos(pi/4+x)+cos(pi/4-x)=sqrt2cos x(i1)sin(7pi/12)cos(pi/4)-cos(7pi/12)sin(pi/4)

Prove that: sin((4 pi)/(9)+7)cos((pi)/(9)+7)-cos((4 pi)/(9)+7)sin((pi)/(9)+7)=(sqrt(3))/(2)