If sinA=1/2,find the value of sin2A and cos2A
Answers
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The value of Sin2A is √3/2 and Cos2A is 1/2.
Given:
SinA = 1/2
Trigonometric formulas.
To find:
Sin2A and Cos2A
Solution:
As we know that here SinA = 1/2. When SinA = 1/2 then we can say that A = 30° since Sin30°=1/2. Now that we know A = 30°, similarly CosA or Cos30° = √3/2.
According to trigonometric formulas Sin2A = 2SinACosA
Substitute the values of SinA and CosA in the formula of Sin2A.
Sin2A = 2 x SinA x CosA
Sin2A = 2 x 1/2 x √3/2
Sin2A = √3/2
Therefore the value of Sin2A is √3/2.
Now that we know the formula of Cos2A = Cos²A - Sin²A or 1 - 2sin²A or 2cos²A - 1
Cos2A = Cos²A - Sin²A
Cos2A = (√3/2)² - (1/2)²
Cos2A = (3/4) - (1/4)
Cos2A = 2/4
Cos2A = 1/2.
Therefore the value of Cos2A is 1/2
The value of Sin2A is √3/2 and Cos2A is 1/2.
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