Answer:
See proof below
Step-by-step explanation:
Just compute left and right sides using a calculator. I am using 4 decimal digits of precision
Left side computations
sin 65° = 0.9063
sin 25° = 0.4226
sin 65° - sin 25°
= 0.9063 - 0.4226
= 0.4837
Right side computation
sin 20° = 0.3420
√2 sin 20° = √2 x 0.3420
= 0.483661..
= 0.4837 (rounded to 4 decimal digits)
Since left side = right side, it is proved that sin 65° - sin 25° = √2 sin 20°
