Submultiple Angle Formulae

The important trigonometrical ratios of submultiple angle formulae are given below:

(i) sin A = 2 sin A2 cos A2

(ii) cos A = cos2 A2 – sin2 A2

(iii) cos  A = 2 cos2 A2 - 1 

(iv) cos A = 1 - 2 sin2 A2 

(v) 1 + cos A = 2 cos2 A2

(vi) 1 - cos A = 2 sin2 A2

(vii) tan2 A21cosA1+cosA

(viii) sin A = 2tanA21+tan2A2

(ix) cos A = 1tan2A21+tan2A2

(x) tan A = 2tanA21tan2A2

(xi) sin A = 3 sin A3 - 4 sin3 A3


(xii) cos A = 4 cos3 A3 - 3 cos A3

(xiii) sin 15° = cos 75° = 3122

(xiv) cos 15° = sin 75° = 3+122

(xv) tan 15° = 2 - √3. 

(xvii) sin 22½˚ = 1222

(xvii) cos 22½˚ = 1222

(xviii) tan 22½˚= √2 - 1. 

(xix) sin 18 ° = cos 72° = 514

(xx) cos 18° = sin 72° = 10+254

(xxi) cos 36° = cos 72° = 5+14

(xxii) sin 36° = cos 54° = 10254

 Submultiple Angles






11 and 12 Grade Math

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