Evaluate the following: `cos(2pi/3)cos(pi/4)-sin(2pi/3)sin(pi/4)`

Evaluate the following limit: (lim)_(x->pi/4)(cos x-sin x)/((pi/4-x)(cos x+sin x))

Prove that: cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

Prove that: cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)="sin"(A+B)

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

Find the principal value of each of the following: (i) cos^(-1)(sin((4pi)/3)) (ii) cos^(-1)(tan((3pi)/4))

Evaluate the following: i) sin\ pi/12 ii) sin\ pi/8 , iii) cos\ pi/8 , iv) cos\ pi/(24

Evaluate the following: i) cos120^(@)sin390^(@)+cos330^(@)cos150^(@) ii) sin^(2)(3pi)/(4)+cos^(2)pi/4+sec^(2)pi/3

Find the principal values of the following : (i) sin^(-1)(sin.(5pi)/(3)) (ii) cos^(-1)cos((4pi)/(3)) (iii) cos [(pi)/(3) + cos^(-1) (-(1)/(2))]

Value of cos^3 (pi/8)cos^3 ((3pi)/8) + sin^3 (pi/8)sin^3 ((3pi)/8) is

If tanA=-3/4 and pi/2 lt A lt pi , find the values of the following: i) sin(A/2) ii) cos(A/2) , iii) tan(A/2)