Question

a) If
A = 60, B = 30°, then prove that
Sin²A - sin² B 8
cos? A cos²B
b) If
Az 60°, B = 450, then
prove that
tan A-tan B = 2-5.
It tan A tanB​

Answer 1

Answer:

See below

Step-by-step explanation:

  Hey there! Thanks for the question!

Given,

A = 60° , B = 30°

To verify : tan(A - B) = tanA-tanB / 1 + tanA tanB.

Now,

tan( 60 - 30 ) = tan60 - tan30 / 1 + tan60° tan30°

We know that, tan30 = 1/√3 , tan60 = √3

tan30° = ( √3) - ( 1/√3) / 1 + ( √3) ( 1/√3)

1/√3 = ( 3 - 1 / √3 ) / 2

1/√3 = 2/√3 / ( 2 )

1/√3 = 1/√3

Both sides of the equation are equal!

Therefore, We proved and verified tan (A-B) = tanA-tanB / 1+ tan A tan B , for A = 60° , B = 30°