Evaluate `|cosalphacosbetacosalphas inbeta-s inalpha-s inbetacosbeta0s inalphacosbetas inalphas inbetacosalpha|`

Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a\ cosalpha,\ a\ s inalpha)a n d\ (a\ cosbeta,\ asinbeta)dot

If s in x+cos x=a, find the value of |s in x-cos x|

Evaluate: int_0^(pi//2)(s in x-cosx)/(1+s in xcosx)dx

Evaluate the following limit: (lim)_(x rarr0)(s in3x-s in x)/(sin x)

Evaluate the following limit: (lim)_(x rarr0)(s in ax+bx)/(ax+s in bx)

Let S={a,b,c}. Find the total number of binary operations on S.

In any triangle ABC, prove that following: a(s in B-s in C)+b(s in C-s in A)+c(s in A-s in B)=0

Evaluate: int_0^(pi//2)(sqrt(s in x))/(sqrt(s in x)+sqrt(cos x))dx

Evaluate the following limit: (lim)_(x rarr0)(tan x-s in x)/(s in3x-xs in x)

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n) then evaluate det[[3,1+s_(1),=alpha^(n)+beta^(n)3,1+s_(1),+s_(2)1+s_(1),1+s_(2),1+s_(3)1+s_(2),1+s_(3),1+s_(4)]]