Question

tan22(1°/2)+tan22(1°/2)/1-(tan22(1°/2))^2 = ?​

Answer 1

Answer:

22½° lies in the first quadrant.

Therefore, tan 22½° is positive.

For all positive values of the angle A we know that, tan A2 = 1−cosA1+cosA−−−−−√

tan 22½° = 1−cos45°1+cos45°−−−−−−√

tan 22½° = 1−12√1+12√−−−−−√, [Since we know that cos 45° = 12√]

tan 22½° = 2√−12√+1−−−−√

tan 22½° = 2√−12√+1⋅2√−12√−1−−−−−−−−−−√

tan 22½° = (2√−1)22−1−−−−−−√

tan 22½° = √2 - 1

Therefore, tan 22½° = √2 - 1