Question

!Помогите с тригонометрией!

2sin31° · cos31°
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sin38° · sin66° · cos38° · sin24°

Answer 1

$frac{2sin31cos31}{sin38sin66+cos38sin24} =frac{sin62}{sin38sin(90-24)+cos38sin24} =frac{sin62}{sin38cos24+cos38sin24} =\ = frac{sin62}{sin(38+24)}= frac{sin62}{sin62} =1$

Answer 2

task/29385289

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2sin31°cos31° / (sin38°sin66° + cos38°sin24°) =

sin62° / (sin38°sin66° +cos38°cos66°) = sin62° / cos(66°-38° ) =

sin62° / cos28° = sin62° /  cos(90°- 62°) = sin62° /  sin62°  =1

ответ: 1.

* * *  P.S.   sin2α =2sinα*cosα  ; cos(α - β) =cosα*cosβ  +sinα*sinα*β ;

sin(90°- α) =cos α  ; cos(90°- α) =sin α   * * *