The value of tan712° is equal to
6+3+2-2
6-3+2-2
6-3+2+2
6-3-2-2
Explanation for the correct option
The given trigonometric expression: tan712°.
It is known that sin(A-B)=sin(A)cos(B)-cos(A)sin(B).
Thus, sin15°=sin45°-30°
⇒sin15°=sin45°cos30°-cos45°sin30°⇒sin15°=12×32-12×12⇒sin15°=322-122⇒sin15°=3-122⇒sin15°=223-1222⇒sin15°=26-28⇒sin15°=6-24
It is known that cos(A-B)=cos(A)cos(B)+sin(A)sin(B).
Thus, cos15°=cos45°-30°
⇒cos15°=cos45°cos30°+sin45°sin30°⇒cos15°=12×32+12×12⇒cos15°=322+122⇒cos15°=3+122⇒cos15°=223+1222⇒cos15°=26+28⇒cos15°=6+24
Now, tanA=sinAcosA.
⇒tanA=2sinAcosA2cos2A⇒tanA=sin2A1+cos2A
Thus, tan712°=sin15°1+cos15°.
⇒tan712°=6-241+6+24⇒tan712°=6-24+6+2⇒tan712°=6-24-6+24+6+24-6+2⇒tan712°=46-2-6-26+216-6+22⇒tan712°=46-42-6+216-6-2-212⇒tan712°=46-42-48-43⇒tan712°=6-2-12-3⇒tan712°=6-2-12+32-32+3⇒tan712°=26-22-2+18-6-34-3⇒tan712°=6-22-2+32-3⇒tan712°=6-3+2-2
Hence, option B is correct.
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