Also, read 
Trigonometry for class 10 
Applications of Trigonometry 
Inverse Trigonometric Function 
Trigonometric formulas:
When you enter in the chapter of trigonometry it seems vast one, but it is not what you believe. This chapter is so much easy to solve. The condition is if you have all the trigonometric formulas on your leaps. The trigonometric formulas include all trigonometric ratios, trigonometric identities, trigonometric sign rule, quadrant rule and some of the value of the trigonometric function of specific degrees.
Here, we listed the important trigonometric formulas:
Basics:
1.Trigonometric Ratios:
Functions  Value 
sin A  \(\frac{P}{H}\) 
cos A  \(\frac{B}{H}\) 
tan A  \(\frac{P}{B}\) 
cosec A  \(\frac{H}{P}\) 
sec A  \(\frac{H}{B}\) 
cot A  \(\frac{B}{P}\) 

Trigonometric formulas based on relations:
Functions  Relations 
tan A  \(\frac{sin\:A}{cos\:A}\) 
cot A  \(\frac{cos\:A}{sin\:A}\) 
sec A  \(\frac{1}{cos\:A}\) 
cosec A  \(\frac{1}{sin\:A}\) 

Negative sign convention of Trigonometric function:
The negative sign (A) has usual meaning in terms of (2π – A).
s.no.  Function 
1.  sin(A) = – sin A 
2.  cos(A) = cos A 
3.  tan(A) = – tan A 
4.  cosec(A) = – cosec A 
5.  sec(A) = sec A 
6.  cot(A) = – cot A 
Also, common used function in quadrants:
The sign convention in these quadrant is remembered as “All School To College”
i.e.
 All positive for 1^{st} quadrant,
 Sin and cosec positive for 2^{nd} quadrant,
 Tan and cot positive for 3^{rd} quadrant,
 Cos and sec positive in 4^{th .}
S.no.  Value 
1.  sin(90⁰A) = cos A 
2.  cos(90⁰A) = sin A 
3.  tan(90⁰A) = cot A 
4.  cosec(90⁰A) = sec A 
5.  sec(90⁰A) = cosec A 
6.  cot(90⁰A) = tan A 

Primary Trigonometric Identities:
s.no.  Identities 
1.  sin^{2 }A + cos^{2} A = 1 
2.  sec^{2 }A – tan^{2} A = 1 
3.  cosec^{2 }A – cot^{2 }A = 1 

Trigonometric Formula As Product Rule:
s.no.  Rules 
1.  sin (A + B) = sin A cos B + cos A sin B 
2.  sin (A – B) = sin A cos B – cos A sin B 
3.  cos (A + B) = cos A cos B – sin A sin B 
4.  cos (A – B) = cos A cos B + sin A sin B 
5.  tan (A + B) = \(\frac{tanA + tanB}{1 – tanA\: tanB}\) 
6.  tan (A – B) = \(\frac{tanA – tanB}{1 + tanA\: tanB}\) 

Trigonometric Formulas for Double Angle:
s.no.  Formulae 
1.  sin 2A = 2 sin A∙cos A 
2.  cos 2A = cos^{2}A – sin^{2}A
=2cos^{2}A – 1 = 1 – 2sin^{2}A 
3.  tan 2A = \(\frac{2tanA}{1 {tan}^{2}A}\) 

Trigonometric Formulas for Triple Angle:
s.no.  Formulae 
1.  Sin 3A = 3sinA – 4sin^{3}A 
2.  Cos 3A = 4cos^{3}A – 3cosA 
3.  Tan3A = \(\frac{3tanA – {tan}^{3}A}{1 3{tan}^{2}A}\) 
4.  Cot3A = \(\frac{{cot}^{3}A – 3cotA}{3{cot}^{2}A – 1}\) 

Trigonometric product conversion:
s.no.  Formulae 
1.  \(\frac{cos(A – B) – cos(A+B)}{2}\) = sinA.sinB 
2.  \(\frac{cos(A – B) + cos(A+B)}{2}\) = cosA.cosB 
3.  \(\frac{sin(A + B) + sin(A – B)}{2}\) = sinA.cosB 
4.  \(\frac{cos(A + B) + sin(A – B)}{2}\) = cosA.sinB 

Extended product rule:
s.no.  Formulae 
1.  sinA.sinB = \(\frac{cos\frac{(A + B)}{2}.cos\frac{(AB)}{2}}{2}\) 
2.  cosA.cosB = \(\frac{cos\frac{(A + B)}{2}.sin\frac{(AB)}{2}}{2}\) 
3.  sinA.cosB = \(\frac{sin\frac{(A + B)}{2}.cos\frac{(AB)}{2}}{2}\) 
4.  cosA.sinB = \(\frac{sin\frac{(A + B)}{2}.sin\frac{(AB)}{2}}{2}\) 

Trigonometric Half Angle Identities:
s.no.  Formulae 
1.  \(\sin\frac{x}{2}=\pm \sqrt{\frac{1\cos\: x}{2}}\) 
2.  \(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\) 
3.  \(\tan(\frac{x}{2}) = \sqrt{\frac{1\cos(x)}{1+\cos(x)}}\)

4.  \(\tan(\frac{x}{2}) = \sqrt{\frac{1\cos(x)}{1+\cos(x)}}\) Also, \(\tan(\frac{x}{2}) =\frac{1\cos(x)}{\sin(x)}\) 
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