Question

(Prove that):
A.
1 - tan 20°. tan 25º = tan 20° + tan 25° ​

Answer 1

Step-by-step explanation:

tan(a+b)= (tan a+tan b)/(1-tan a tan b)

tan(20°+25°)= (tan 20+ tan25)/(1-tan20.tan25)

tan 45°= (tan 20+ tan25)/(1-tan20.tan25)

1=(tan 20+ tan25)/(1-tan20.tan25)

1 - tan20°.tan25°= tan 20°+ tan 25°

Answer 2

Step-by-step explanation:

formula

$\tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) }$

$\alpha = 20 \: \: and \: \beta = 25$

$\tan( 20 + 25 ) = \frac{ \tan( 20 ) + \tan( 25 ) }{1 - \tan( 20 ) \tan( 25) }$

$\tan( 45 ) = \frac{ \tan( 20 ) + \tan( 25 ) }{1 - \tan( 20 ) \tan( 25) }$

$we \: know \: that \: \tan(45) = 1$

$1 = \frac{ \tan( 20 ) + \tan( 25 ) }{1 - \tan( 20 ) \tan( 25) }$

${ \tan( 20 ) + \tan( 25 ) } = {1 - \tan( 20 ) \tan( 25) }$