TRIGONOMETRY FORMULAS

Trigonometry


Trigonometry is an important chapter of Mathematics for the level of class 10 and 12 and often children are confuses regarding the formulas of this chapter. Here is a chapter wise list of all the trigonometric formulas which are widely required while doing the sums of Trigonometry. 

Formulas for Compound Angles of trigonometry


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.
sin (A + B).sin (A - B) = sin^2 A- sin^2 B.
sin (A + B).sin (A - B) = cos^2 B - cos^2 A.
cos (A + B).cos (A - B) = cos^2 A - sin^2 B.
cos (A + B).cos (A - B) = cos^2 B - sin^2 A.
tan (A + B) = {tan A + tan B}/{1 - tan A.tan B}.
tan (A - B) = {tan A - tan B}/{1 + tan A.tan B}.
cot (A + B) = {cot A.cot B - 1}/{cot B + cot A}.
cot (A - B) = {cot A.cot B + 1}/{cot B - cot A}.
tan (A + B + C) = {tan A + tan B + tan C - tan A.tan B.tan C}/{1 - tan A.tan B - tan B.tan C -tan C.tan A}.

Formulas for sums & products of trigonometry


sin C + sin D = 2.sin {(C + D)/2}.cos {(C - D)/2}.
sin C - sin D = 2.cos {(C + D)/2}.sin {(C - D)/2}.
cos C + cos D = 2.cos {(C + D)/2}.cos {(C - D)/2}.
cos C - cos D = 2.sin {(C + D)/2}.sin {(D - C)/2}.
2.sin A.cos B = sin (A + B) + sin (A - B).
2.cos A.sin B = sin (A + B) - sin (A - B).
2.cos A.cos B = cos (A + B) + cos (A - B).
2.sin A.sin B = cos (A - B) + cos (A + B).

Formulas for Multiple angles of trigonometry


sin 2a = 2.sin a.cos a.
cos 2a = cos ^2 a - sin^2 a.
cos 2a = 2cos^2 a - 1.
cos 2a = 1- 2sin^2 a.
1 + cos 2a = 2 cos^2 a.
1 - cos 2a= 2 sin^2 a.
tan^2 a = (1 - cos 2a)/(1 + cos 2a).
sin 2a = 2tan a/(1 + tan^2 a).
cos 2a = (1 - tan^2 a)/(1 + tan^2 a).
tan 2a = 2.tan a/(1 - tan^2 a).
sin 3a = 3.sin a - 4.sin^3 a.
cos 3a = 4.cos^3 a - 3.cos a.
tan 3a = (3 tan a - tan^3 a)/(1-3tan^2 a).

Trigonometric Formula

Useful trig formulas and some very helpful links for learning trigonometric concepts.



Triangle ABC is any triangle with side lengths a,b,c
Law of Cosines

Law of Sines

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