Question

Evaluate Cos22 1/2°÷sin671/2°??

Answer 1

cos (2θ) = 2 cos² θ - 1 ... [trig identity]

22.5° * 2 = 45°

so cos 45° = 2 cos² 22.5° - 1

2 cos² 22.5° = 1 + cos 45°

2 cos² 22.5° = 1 + (1 / √2) = [(√2 + 1) / √2] ... [taking a common denominator]

cos² 22.5° = [(√2 + 1) / √2] / 2

cos² 22.5 = [(√2 + 1) / (2√2)] ... [division by 2 is the same as multiplying by 1/2]

cos 22.5° = √[(√2 + 1) / (2√2)] ←←[exact answer ... so leave it like that]

the sine of an angle equals the cosine of the angle's complement

so sin 67.5° = cos (90 - 67.5) = cos 22.5° = √[(√2 + 1) / (2√2)]

hope it works pls mark it brainliest