Question

If msin theta= ncos theta show that ; tan theta + cot theta / tan theta - cot theta = nsin theta + mcos theta / nsin theta - mcos theta = n square + m square / n square - m square.

Answer 1

Given:msinθ=ncosθ⇒tanθ=nm   ...(1)⇒cotθ=mn    ....(2)To prove: tanθ+cotθtanθ−cotθ=nsinθ+mcosθnsinθ−mcosθ=n2+m2n2−m2Consider,nsinθ+mcosθnsinθ−mcosθ=n(sinθncosθ)+m(cosθncosθ)n(sinθncosθ)−m(cosθncosθ)=tanθ+mntanθ−mn=tanθ+cotθtanθ−cotθ    [Using 2]