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Question

tan712°=?


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Solution

tan712°=sin712°cos712°

=sin2712°sin712°cos712°

=2sin2712°2sin712°cos712°

=1-cos15°sin15° [1-cos2A=2sin2A,2sinAcosA=sin2A]

=1-cos(45°-30°)sin45°-30°

=1-cos45°cos30°-sin45°sin30°sin45°cos30°-cos45°sin30°

=1-12×32-12×1212×32-12×12

=1-3+1223-122

=22-3-1223-122

=22-3-13-1

=22-3-13-1×3+13+1

=26-3-3+22-3-132-12

=26-23+22-43-1

=26-3+2-22

=6-3+2-2

Hence, tan712°=6-3+2-2


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