Rumus Identitas Sudut Kelipatan Setengah

Rasio trigonometri penting dari rumus sudut kelipatan setengah diberikan di bawah ini:

(i) sin A = 2 sin $\frac{A}{2}$ cos $\frac{A}{2}$

(ii) cos A = $cos^2 \frac{A}{2}-sin^2 \frac{A}{2}$

(iii) cos A = 2 $cos^2 \frac{A}{2}$ - 1

(iv) cos A = 1 - 2 $sin^2 \frac{A}{2}$

(v) 1 + cos A = 2 $cos^2 \frac{A}{2}$

(vi) 1 - cos A = 2 $sin^2 \frac{A}{2}$

(vii) $tan^2 \frac{A}{2}=\frac{1-cosA}{1+cosA}$

viii) sin A $=\frac{2tan\frac{A}{2}}{1+tan^2 \frac{A}{2}}$

(ix) cos A $=\frac{1-tan^2 \frac{A}{2}}{1+tan^2 \frac{A}{2}}$

(x) tan A $=\frac{2tan\frac{A}{2}}{1-tan^2 \frac{A}{2}}$

(xi) sin A $=3 sin\frac{A}{3}-4sin^3 \frac{A}{3}$

(xii) cos A $=4cos^3 \frac{A}{3}-3 cos\frac{A}{3}$

(xiii) sin 15° = cos 75°$=\frac{\sqrt{3}-1}{2\sqrt{2}}$

(xiv) cos 15° = sin 75° $=\frac{\sqrt{3}+1}{2\sqrt{2}}$

(xv) tan 15° $=2-\sqrt{3}$

(xvii) sin 22½˚ $=\frac{1}{2}\sqrt{2-\sqrt{2}}$

(xvii) cos 22½˚ $=\frac{1}{2}\sqrt{2+\sqrt{2}}$

(xviii) tan 22½˚$=\sqrt{2}-1$

(xix) sin 18 ° = cos 72° $=\frac{\sqrt{5}-1}{4}$

(xx) cos 18° = sin 72° $=\frac{\sqrt{10+2\sqrt{5}}}{4}$

(xxi) cos 36° = cos 72° $=\frac{\sqrt{5}+1}{4}$

(xxii) sin 36° = cos 54° $=\frac{\sqrt{10-2\sqrt{5}}}{4}$