Question

prove that tan theta + cot theta equals sec theta/sin theta

Answer 1

Answer:

Step-by-step explanation:

$LHS = tan \theta + cot\theta$

       =  $\frac{1}{cot\theta}+cot\theta$

       = $\frac{1+cot^{2}\theta }{cot\theta}$

       = $\frac{cosec^{2}\theta }{cot\theta}$

       = $\frac{\frac{1}{sin^{2}\theta } }{\frac{cos\theta}{sin\theta} }$

       = $\frac{1}{sin^{2}\theta }$ x $\frac{sin\theta}{cos\theta}$

       = $\frac{1}{sin\theta}$ x $\frac{1}{cos\theta}$

       = $\frac{1}{sin\theta}$ x $sec\theta$

       = $\frac{sec\theta}{sin\theta}$

       $= RHS$ proved

Answer 2

Step-by-step explanation:

prove that tan theta + cot theta equals sec theta/sin theta