[" (1) "92cos x=-(1)/(3)" and "pi

The value of x satisfying the equation (sin^(-1)x)^(3)-(cos^(-1)x)^(3)+(sin^(-1)x)(cos^(-1)x)(sin^(-1)x-cos^(-1)x)=(pi^(3))/(16) is : (a) "cos"(pi)/(5) (b) "cos"(pi)/(4) (c) "cos"(pi)/(8) (d) "cos"(pi)/(12)

Solve : sin ^(-1) x+sin ^(-1) ""y=(2pi)/(3) and cos ^(-1) x- cos ^(-1)y =(pi)/(3).

int_(0)^(1)(cos x)/(1+x)dx=k and int_(6 pi-3)^(6 pi)(cos((x)/(3)))/(6 pi+3-x)dx=mk

The solution set of "sin" (x - (pi)/(4))-"cos" (x + (3 pi)/(4)) =1 " and " (2 "cos" 7x)/("cos" 3 + "sin" 3) gt 2^("cos" 2x) , is

The solution set of "sin" (x - (pi)/(4))-"cos" (x + (3 pi)/(4)) =1 " and " (2 "cos" 7x)/("cos" 3 + "sin" 3) gt 2^("cos" 2x) , is

int _ (- 1) ^ ((3) / (2)) | x sin pi x | dx = [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (- 1) ^ (1) - [(- x cos pi x) / (pi) + (sin pi x) / (pi ^ (2))] _ (1) ^ ((3) / (2) )

The number of solution for , {:(sin(x-(pi)/4)-cos(x+(3pi)/4)=1),(" "(2cos 7x)/(cos 3+sin3) gt 2^(cos 2x)):}}" in" (0,2pi) is

sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)