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Exact Value of tan 11¼°

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°

= 1cos22½°sin22½°

= 11+cos45°21cos45°2

= 21+cos45°1cos45°

= 21+12112

= 22+12212

= 222+121

= 222+121 × 2+12+1

= 222+1(2+1)2(2+1)(21)

= 22(2+1)(2+1)21

= 4+22(2+1)

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11 and 12 Grade Math

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