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Trigonometric Functions of A in Terms of cos 2A

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



● Multiple Angles





11 and 12 Grade Math

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