(tan(x-(pi)/(2))*cos((3 pi)/(2)+x)-sin^(3)((7 pi)/(2)-x))/(cos(x-(pi)/(2))*tan((3 pi)/(2)+x))

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

The expression (tan(x-(pi)/(2)).cos((3pi)/(2)+x)-sin^(3)((7pi)/(2)-x))/(cos(x-(pi)/(2)).tan((3pi)/(2)+x)) simplifies to

The expression (tan(x-pi/2)cos((3pi)/2+x)-sin^3((7pi)/2-x))/(cos(x-pi/2)tan((3pi)/2+x) is equal to

cos((3pi)/(2) +x) cos(2pi+x)[cot(3pi)/(2)-x+cot(2pi+x)]=1

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (1)((pi)/(4),(pi)/(2))(2)(-(pi)/(2),(pi)/(4))(3)(0,(pi)/(2))(4)(-(pi)/(2),(pi)/(2))^(((pi)/(4)),(pi)/(2))^(((pi)/(4)))(2)

Show that cos ^(2) x+cos ^(2)(x+(pi)/(3))+cos ^(2) (x-(pi)/(3))=(3)/(2)

If x=sin(theta+(7 pi)/(12))+sin(theta+(pi)/(12))+sin(theta+(3 pi)/(12))Y=cos(theta+(7 pi)/(12))+cos(theta+(pi)/(12))+cos(theta+(3 pi)/(12)) then prove that (X)/(Y)-(Y)/(X)=2tan2 theta

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

Prove that cos^(2)x+cos^(2)(x+(pi)/(3))+cos^(2)(x-(pi)/(3))=(3)/(2)