Evaluate `|[cos alpha cos beta,cos alpha sin beta,-sin alpha],[-sin beta,cos beta,0],[sin alpha cos beta,sin alpha sin beta,cos alpha]|`

The value of the determinant Delta = |(cos (alpha + beta),- sin (alpha + beta),cos 2 beta),(sin alpha,cos alpha,sin beta),(- cos alpha,sin alpha,- cos beta)| , is

The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin alpha hatk is a

Let f(alpha, beta) = =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)| if i =int_(-pi//2)^(pi//2) cos ^(2)beta(f(0,beta)+f(0,(pi)/(2)-beta))dbeta then i is

Let f(alpha, beta) =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)| The value of l=int_(0)^(pi//2)e^(beta)(f(0,0)+f((pi)/(2),beta)+f((3pi)/(2),(pi)/(2)-beta))dbeta is

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)