tell important formulas in trigonometry
for class 10
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Trigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, function, identities, formulas to solve problems based on it, especially for right-angled triangles. Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design. This chapter is very important as it comprises many topics like Linear Algebra, Calculus and Statistics.
Trigonometry is introduced in CBSE class 10. It is a completely new and tricky chapter where one needs to learn all the formula and apply them accordingly. Trigonometry Class 10 formulas are tabulated below.
List of Trigonometric Formulas for 10th
Trigonometry Formulas for Class 10
Applying Pythagoras theorem for the given right-angled triangle, we have:
(Perpendicular)2+(Base)2=(Hypotenuse)2
⇒(P)2+(B)2=(H)2
The Trigonometric formulas are given below:
S.no Property Mathematical value
1 sin A Perpendicular/Hypotenuse
2 cos A Base/Hypotenuse
3 tan A Perpendicular/Base
4 cot A Base/Perpendicular
5 cosec A Hypotenuse/Perpendicular
6 sec A Hypotenuse/Base
Reciprocal Relation Between Trigonometric Ratios
S.no Identity Relation
1 tan A sin A/cos A
2 cot A cos A/sin A
3 cosec A 1/sin A
4 sec A 1/cos A
Trigonometric Sign Functions
sin (-θ) = − sin θ
cos (−θ) = cos θ
tan (−θ) = − tan θ
cosec (−θ) = − cosec θ
sec (−θ) = sec θ
cot (−θ) = − cot θ
Trigonometric Identities
sin2A + cos2A = 1
tan2A + 1 = sec2A
cot2A + 1 = cosec2A
Periodic Identities
sin(2nπ + θ ) = sin θ
cos(2nπ + θ ) = cos θ
tan(2nπ + θ ) = tan θ
cot(2nπ + θ ) = cot θ
sec(2nπ + θ ) = sec θ
cosec(2nπ + θ ) = cosec θ
Complementary Ratios
Quadrant I
sin(π/2−θ) = cos θ
cos(π/2−θ) = sin θ
tan(π/2−θ) = cot θ
cot(π/2−θ) = tan θ
sec(π/2−θ) = cosec θ
cosec(π/2−θ) = sec θ
Quadrant II
sin(π−θ) = sin θ
cos(π−θ) = -cos θ
tan(π−θ) = -tan θ
cot(π−θ) = – cot θ
sec(π−θ) = -sec θ
cosec(π−θ) = cosec θ
Quadrant III
sin(π+ θ) = – sin θ
cos(π+ θ) = – cos θ
tan(π+ θ) = tan θ
cot(π+ θ) = cot θ
sec(π+ θ) = -sec θ
cosec(π+ θ) = -cosec θ
Quadrant IV
sin(2π− θ) = – sin θ
cos(2π− θ) = cos θ
tan(2π− θ) = – tan θ
cot(2π− θ) = – cot θ
sec(2π− θ) = sec θ
cosec(2π− θ) = -cosec θ
Sum and Difference of Two Angles
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) = [(tan A + tan B)/(1 – tan A tan B)]
tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]
Double Angle Formulas
sin2A = 2sinA cosA = [2tan A + (1+tan2A)]
cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
tan 2A = (2 tan A)/(1-tan2A)
Thrice of Angle Formulas
sin3A = 3sinA – 4sin3A
cos3A = 4cos3A – 3cosA
tan3A = [3tanA–tan3A]/[1−3tan2A
Step-by-step explanation:
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