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How to find the exact value of tan 11¼° using the value of cos 45°?
Solution:
For all values of the angle A we know that, 2 sin2 A2 = 1 - cos A
Again, for all values of the angle A we know that, 2 sin A2 cos A2 = sin A
Now tan 11¼°
= sin11¼°cos11¼°
= sin11¼°cos11¼° × 2sin11¼°2sin11¼°
= 2sin211¼°2sin11¼°cos11¼°
= 1−cos22½°sin22½°
= 1−√1+cos45°2√1−cos45°2
= √2−√1+cos45°√1−cos45°
= √2−√1+1√2√1−1√2
= √2−√√2+1√2√√2−1√2
= √2√2−√√2+1√√2−1
= √2√2−√√2+1√√2−1 × √√2+1√√2+1
= √2√2⋅√√2+1−√(√2+1)2√(√2+1)(√2−1)
= √2√2(√2+1)−(√2+1)√2−1
= √4+2√2−(√2+1)
11 and 12 Grade Math
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