Question

Prove that Cos theta/ 1+ tan theta + sin theta /1- cot theta = sin beta + cos theta

Answer 1

LHS = $\frac{cos\theta}{1-\frac{sin\theta}{cos\theta} } + \frac{sin\theta}{1-\frac{cos\theta}{sin\theta} }$

      = $\frac{cos^{2}\theta }{cos\theta-sin\theta} + \frac{sin^{2} \theta}{sin\theta-cos\theta}$

     = $\frac{cos^{2}\theta -sin^{2}\theta }{cos\theta-sin\theta}$

     = $\frac{(cos\theta-sin\theta )(cos\theta+sin\theta)}{cos\theta-sin\theta}$

    = $cos\theta + sin\theta$(Prooved)