cos@ / sin@ = -p/q
multiply by cos@/sin@ on both the sides and apply componendo dividendo,
=> (p cos@ - q sin@)/(p cos@ + q sin@) = 1/ cos 2@ = p2 + q2 / p2-q2
If cotθ = - p/q, then the value of (p cosθ - q sinθ)/(p cosθ + q sinθ) is
cos@ / sin@ = -p/q
multiply by cos@/sin@ on both the sides and apply componendo dividendo,
=> (p cos@ - q sin@)/(p cos@ + q sin@) = 1/ cos 2@ = p2 + q2 / p2-q2