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8. Simplify
2 tan 2212
1 - tan22 12°
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thnku
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
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