Question

(1 + tan 2A)(1 - sin A) (1 + sin A) = 1​

Answer 1

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

hope it helps you.

Answer 2

(

1

+

tan

2

A

)

(

1

−

sin

A

)

(

1

+

sin

A

)

=  

sec

2

A

(

1

−

sin

2

A

)

=  

1

cos

2

A

×

cos

2

A

=  

1