Question

show that:
sin(45+A)×(sin45-A)=1/2cos2A
pls ans fast​

Answer 1

Step-by-step explanation:

sin (45°+A) × sin (45°–A)

= ( sin 45°cos A + cos 45°sin A)×( sin 45°cos A – cos 45°sin A)

= ( sin²45°cos²A – cos²45°sin²A)

= (1/2 cos²A – 1/2 sin²A)

= 1/2 (cos²A–sin²A)

= 1/2 cos 2A