Trigonometric Ratios of Multiple Angles
If A is an angle, then 2A, 3A, 4A, 5A,
etc are called multiple angles of A. In this section we will discuss about the trigonometric ratios of multiple angles
2A and 3A in terms of A.
Trigonometric Ratios of Angle 2A in terms of A
Formula for sin2A
Formula for cos2A
Formula for tan2A and cot2A
Some Useful Results
Trigonometric Ratios of Angle 3A in terms of A
List of trigonometric formula for multiple angles 2A and 3A:
Geometrical Proof of 2A Formulae
Let O be the centre of the circle ABC and AB be a
diameter (In the given figure below.). Let ∠CAB = A, then ∠COB = 2A [∵ Central angle is double of inscribed angle on same arc.]. ∠ACB = 90° [Inscribed angle
on semi-circle.]
Let CM is perpendicular to AB. Then, ∠ACM = 90° – A, and hence ∠BCM = A.
Now from the right angle ΔOMC,
Worked Out Examples:
You can comment your questions or problems regarding the
trigonometric ratios of multiple angles.
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