Trigonometry & Algebra ~ My Profile

$\sin^{2} θ + \cos^{2} θ = 1$

$\tan^{2} θ + 1 = \sec^{2} θ$

$\cot^{2} θ + 1 = c o s e c^{2} θ$

sin(−θ)=−sinθ
tan(−θ)=−tanθ
cot(−θ)=−cotθ
cos(−θ)=cosθ
sec(−θ)=secθ

$\sin (A + B) = \sin A \cos B + \cos A \sin B$

$\sin (A - B) = \sin A \cos B - \cos A \sin B$

$\cos (A + B) = \cos A \cos B - \sin A \sin B$

$\cos (A - B) = \cos A \cos B + \sin A \sin B$

$\tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$

$\tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$

$\sin A s i n B = \frac{1}{2} [\cos (A - B) - \cos (A + B)]$

$\cos A \cos B = \frac{1}{2} [\cos (A - B) + \cos (A + B)]$

$\sin A \cos B = \frac{1}{2} [\sin (A + B) + \sin (A - B)]$

$\cos A \sin B = \frac{1}{2} [\sin (A + B) - \sin (A - B)]$

$\sin A + \sin B = 2 \sin (\frac{A + B}{2}) \cos (\frac{A - B}{2})$

$\sin A - \sin B = 2 \cos (\frac{A + B}{2}) \sin (\frac{A - B}{2})$

$\cos A + \cos B = 2 \cos (\frac{A + B}{2}) \cos (\frac{A - B}{2})$

$\cos A - \cos B = - 2 \sin (\frac{A + B}{2}) \sin (\frac{A - B}{2})$

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

$\cos 2 A = \cos^{2} A - \sin^{2} A = 1 - 2 s i n^{2} A = 2 c o s^{2} A - 1 = \frac{1 - \tan^{2} A}{1 + \tan^{2} A}$

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

$\sin 3 A = 3 \sin A - 4 \sin^{3} A = 4 \sin (60^{\circ} - A) . \sin A . \sin (60^{\circ} + A)$

$\cos 3 A = 4 \cos^{3} A - 3 \cos A = 4 \cos (60^{\circ} - A) . \cos A . \cos (60^{\circ} + A)$

tan3A=3tanA–tan3A1−3tan2A

(x + a) (x + b) = x2 + (a + b) x + ab

(x – a) (x – b) = x2 – (a + b) x + ab

$\sin 3 A = 3 \sin A - 4 \sin^{3} A = 4 \sin (60^{\circ} - A) . \sin A . \sin (60^{\circ} + A)$

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