Question

Simplify (sec theta + tan theta)(1- sin theta)

Answer 1

hope it is helpful

sin^2theta+cos^2theta=1

Answer 2

$\huge\bf{Answer-}$

$\large\sf{=(\sec \theta + \tan \theta) (1 - \sin \theta ) }$

$\large\sf{=(\frac{1}{\cos \theta}+\frac{\sin \theta}{\cos \theta})(1- \sin \theta) }$

$\large\sf{=(\frac{1 + \sin \theta}{\cos \theta})(1 - \sin \theta)}$

$\large\sf{=\frac{{(1)}^{2} - {(\sin \theta)}^{2}}{\cos \theta }}$

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

$\large\sf{=\frac{{\cos}^{2}\theta}{\cos \theta}}$

$\large\sf{=\cos \theta}$