Question

1 minus sin theta into 1 + sin theta is equal to 1 by sec square theta prove that question

Answer 1

Question : Prove that $(1 - \sin \theta)(1 + \sin \theta)$ = $\frac{1}{(sec \theta)^2 }$

Proof :

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

Identities used :

• (a + b)( a - b) = a^2 - b^2

• sin^2 x +cos^2 x = 1 ;

• 1 - sin^2 x = cos^2 x

• cosx = 1/secx