Question

sin( 45 degre +A)( sin 45 degre - A) is equal to​

Answer 1

Answer:

sin(45° + A) sin(45° - A)

Sin (A ± B) = sin A cos B ± cos A sin B

(sin 45° cos A + cos 45° sin A) (sin 45° cos A - cos 45° sin A)

This is in the form of (a + b) (a - b)

Therefore

(sin 45° cos A)² - (cos 45° sin A)²²

cos² A - sin² A

         2

cos 2A

    2

Answer 2

sin(A+B)×sin(A-B)=sin²A-sin²B

now,

sin(45+A)×sin(45-A)=

sin²45-sin²A=

(1/√2)²--sin²A

=1/2 --sin²A=>

(1-2sin²A)/2=

===>(cos2A)/2. ....ans