State if the given angles are coterminal. (i) `alpha=185^0,beta=-545^0` (ii) `alpha=(17pi)/(36),beta=(161pi)/(36)`

State if the given pairs of angles are coterminal. (a) -185^@,535^@" (b) "1000^@,270^@" (c ) "(15pi)/4,-(17pi)/4

If the three points (a,b), (a+kcosalpha,b+ksinalpha)and(a+kcosbeta,b+ksinbeta) are the vertices of an equilateral triangle , then which of the following is true and why ? (i) |alpha-beta|=(pi)/(4) , (ii) |alpha-beta|=(pi)/(2) (iii) |alpha-beta|=(pi)/(6) , (iv) |alpha-beta|=(pi)/(3)

If tan((alpha pi)/4)=cot((beta pi)/4) then

Prove that cos (alpha+beta) +sin (alpha-beta)=2sin(pi/4+alpha)cos(pi/4+beta)

If alpha and beta are the complex cube roots of 1 show that, alpha^(4)+beta^(4)+alpha^(-1).beta^(-1)=0.

If alpha , beta be the imaginary cube root of unity, then show that alpha^4+beta^4+ alpha^-1beta^-1=0

If alpha, beta be the roots of the equation x^(2)+x+1=0 , the value of alpha^(4)beta^(4)-alpha^(-1)beta^(-1) is

Let alpha, beta be such that pi lt alpha lt beta lt 3pi, if sin alpha + sin beta =- (21)/(65) and cos alpha + cos beta =(27)/(65), then the value of cos ""(alpha - beta)/(2) is-

If cos beta is the geometric mean of sin alpha and cos alpha, then show that cos 2 beta= -2 cos^(2) ((pi)/(4)+alpha)

If 0 < alpha < pi/ 6 then alpha(cosec alpha) is