Question

Show that : cos $\theta$ (tan $\theta$ + 2 ) (2 tan $\theta$ +1 ) = 2 sec $\theta$ + 5 sin $\theta$

Answer 1

L.H.S = cos $\theta$ (2 ${\tan }^2$ $\theta$ + 5 tan $\theta$ + 2 )

= cos $\theta$ [ 2 (${\tan }^2$$\theta$ + 1 ) + 5 tan$\theta$ ]

= cos $\theta$ (2 ${\sec }^2$ $\theta$ + 5 tan $\theta$ ) = cos $\theta$ $(\frac{2}{co{s}^2\theta }+5\frac{sin\theta }{cos\theta })$

= 2sec$\theta$ + 5 sin $\theta$ = R.H.S