Question

(1 + tan² A) (1 - sin A) (1 + sin A) = 1​

Answer 1

Answer:

LHS :

(1 + tan^2 A) (1 - sin A) (1 + sin A)

= sec^2 A (1 - sin^2 A)

= sec^2 A × cos^2 A (sin^2 A + cos^2 A = 1, So 1 - sin^2 A = cos^2 A)

= 1 × cos^2 A

______

cos^2 A

= 1 = RHS

Proved

Hope it helps.

Answer 2

Answer:

$(1 + \tan {}^{2} a)(1 - \sin \: a)(1 + \sin \: a) = 1$

$(1 + \tan {}^{2} a )(1 - \sin {}^{2} a) = 1$

$(1 + \tan {}^{2} a)( \sin{}^{2} a + \cos {}^{2} a - \sin {}^{2}a) = 1$

$(1 + \tan {}^{2} a)( \cos {}^{2} a) = 1$

$( \cos {}^{2} a + \tan {}^{2} a \times \cos {}^{2} a) = 1$

$\cos {}^{2} a + \frac{ \sin {}^{2} a }{ \cos {}^{2} a} \times \cos {}^{2} a = 1$

$sin {}^{2} a + cos {}^{2} a = 1$

$1 = 1$

hence proved