The expression using trigonometric identities = cos 2y = 2cos²A-1
y = 22.62° (quadrant 1)
Further explanation
Trigonometry is the science of mathematics that studies the relationship between sides and angles in triangles
Trigonometric identity is a sentence that contains trigonometric functions. The truth of this sentence is an identity that needs to be proven
There are several kinds of identity formulas that can be used
Double angle is multiplication of angles with integers
The value of the dual angle function can be derived from the trigonometric function of an angle. The relationship between the two can be obtained from the sum of the angles
Trigonometry Formulas for Double Angles:
sin 2A = 2 sin A cos A
cos 2A = 1 - 2 sin²A = 2cos²A-1
tan 2A = 2 tan A / 1-tan²A
In the task it is known that the value of sec (y) = 13/12, because
[tex]sec (y) = \frac{1}{cos\:y}[/tex]
then [tex]cos\:y=\frac{12}{13}[/tex]
so
[tex]cos\:2y\:=\:2(\frac{12}{13})^2 - 1[/tex]
[tex]cos\:2y=\:\frac{119}{169}[/tex]
cos 2y = 0.704
2y = 45.239°
y = 22.62° ( y lie between 0 and π/2)
Learn more
trigonometric ratio
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Use Pythagoras' theorem
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the triangle angle
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Keywords: trigonometric identities, sin, cos
