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We will learn how to express trigonometric functions of A in terms of cos 2A or trigonometric ratios of an angle A in terms of cos 2A.
We know the formula of cos 2A and now we will apply the formula to proof the below trigonometric ratio of multiple angle.
(i) Prove that: cos2 A = 1+cos2A2 i.e., cos A = ±√1+cos2A2
We know that, cos 2A = 2 cos^2 A - 1
⇒ cos2 A = 1+cos2A2
i.e., cos A = ±√1+cos2A2
(ii) Prove that: sin2
A = 1−cos2A2 i.e., sin A
= ±√1+cos2A2
We know that, cos 2A = 1 - 2 sin^2 A
⇒ sin2 A = 1−cos2A2
i.e., sin A = ±√1+cos2A2
(iii) Prove that: tan2 A = 1−cos2A1+cos2A i.e., tan A = ±√1−cos2A1+cos2A
We know that, tan2 A = sin2Acos2A
⇒ 1−cos2A1+cos2A
i.e., tan A = ±√1−cos2A1+cos2A
11 and 12 Grade Math
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