If `A = [(0,-tan(alpha//2)),(tan(alpha//2),0)]` and l is a `2xx2` unit matrix, prove that
`l+A(l-A)[(cosalpha,-sinalpha),(sinalpha,cosalpha)]`

If A=[(cas alpha, sinalpha),(-sinalpha,cosalpha)], AA'=

If A=[(0,-tan (alpha/2)),(tan (alpha/2),0)] and I is 2 xx 2 unit matrix, then (I-A)[(cos alpha,-sin alpha),(sin alpha, cos alpha)] is

Prove that sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1 .

If tan alpha=(1)/(7), tan beta=(1)/(3), then cos 2 alpha is equal to

If alpha is a complex number such that alpha^(2)+alpha+1=0 then alpha^(31) is

Find the integrals of the functions (cos2x-cos2alpha)/(cosx-cosalpha)

If alpha , beta are the roots of the equation 1 + x + x^(2) = 0 , then the matrix product [{:( 1 , beta) , (alpha , alpha):}] [{:(alpha , beta) , (1 , beta):}] is equal to

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

The expression tan ^(2) alpha+cot ^(2) alpha is