Question

Show that (Seco +Tano) (1-Sino) = Cos0​

Answer 1

Using LHS:

$\\\tt (sec \theta + tan \theta)(1-sin \theta) \\\tt = (\dfrac{1}{cos \theta} + \dfrac{sin \theta}{cos \theta}) (1-sin \theta) \\\tt = \dfrac{1+sin \theta}{cos \theta} (1-sin \theta) \\\tt = \dfrac{1-sin^2 \theta}{cos \theta}$

Using trigonometric identity:

$\\\tt sin^2 a + cos^2a =1$

We have:

$\\\tt \dfrac{cos^2 \theta}{ cos \theta} \\\tt = cos \theta$

Hence proved.