Simplify the following. `(Cos alpha + i Sin alpha)^4/(Cos alpha- iSin alpha)^3`

Simplify the following. (Cos 5alpha + i Sin 5alpha) / (Cos alpha + i Sin alpha)

Simplify the following. ((Cos 3theta - iSin 3theta) ( Cos 2theta + i Sin 2theta)) /((Cos 4theta + i Sin 4theta)^6 (Cos theta + i Sin theta)^6)

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

If (2sin alpha)/({1+cos alpha + sin alpha})=y, then ({1-cos alpha+sin alpha})/(1+sin alpha)=

Eliminate alpha , if x = r cos alpha , y = r sin alpha .

If p & q are lengths of perpendicular from the origin x sin alpha + y cos alpha = a sin alphacos alpha and x cos alpha-y sin alpha = acos 2alpha, then 4p^2 + q^2

The difference of the tangents of the angles, which the lines (tan^(2) alpha+cos^(2) alpha)x^(2)-2xy tan alpha + sin^(2) alpha" "y^(2)=0 make with the X-axis, is