!Помогите с тригонометрией! 2sin31° · cos31° ------------------------------------------- sin38° · sin66° · cos38° · sin24°. Created by kas2punk. matematika-ru

!Помогите с тригонометрией! 2sin31° · cos31° -----------------------------------...

March 2022 2 22 Report

!Помогите с тригонометрией!

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

Хуqожнuк

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 * * *

3 votes Thanks 2

oganesbagoyan

Verified answer

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

2 votes Thanks 2

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