Please give all formula of trigonometry ?

Question

Answer

Answer

Pythagoras theorem and some other identities

a2 + b2 = c2

Sin ² θ + Cos ² θ = 1.

Tan 2 θ + 1 = Sec2 θ

Cot2 θ + 1 = Cosec2 θ

Sin 2θ = 2 sin θ cos θ

Cos 2θ = cos² θ – sin² θ

Tan 2θ = 2 tan θ / (1 – tan² θ)

Cot 2θ = (cot² θ – 1) / 2 cot θ

Answer

Answer

Cos^2+sin^2=1
tan^2+1=sec^2
cot^2+1=cosec^2

Answer

Introduction to Trigonometry:
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is widely used in various fields such as physics, engineering, and navigation. Trigonometry helps us understand and calculate the properties of triangles and the measurements of angles.

Trigonometric Ratios:
Trigonometric ratios are six ratios that relate the sides of a right triangle to its angles. These ratios are sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). Let's explore each of these trigonometric ratios:

Sine (sin):
Sine is defined as the ratio of the length of the side opposite an acute angle to the hypotenuse of a right triangle. It is denoted as sin(A) = opposite/hypotenuse.

Cosine (cos):
Cosine is defined as the ratio of the length of the adjacent side to the hypotenuse of a right triangle. It is denoted as cos(A) = adjacent/hypotenuse.

Tangent (tan):
Tangent is defined as the ratio of the length of the side opposite an acute angle to the length of the adjacent side of a right triangle. It is denoted as tan(A) = opposite/adjacent.

Cosecant (cosec):
Cosecant is the reciprocal of sine. It is defined as the ratio of the hypotenuse to the length of the side opposite an acute angle. It is denoted as cosec(A) = 1/sin(A).

Secant (sec):
Secant is the reciprocal of cosine. It is defined as the ratio of the hypotenuse to the length of the adjacent side. It is denoted as sec(A) = 1/cos(A).

Cotangent (cot):
Cotangent is the reciprocal of tangent. It is defined as the ratio of the adjacent side to the length of the side opposite an acute angle. It is denoted as cot(A) = 1/tan(A).

Trigonometric Formulas:
Trigonometry involves various formulas that help in solving problems related to triangles and angles. Here are some commonly used trigonometric formulas:

1. Pythagorean Identity:
- sin^2(A) + cos^2(A) = 1
- 1 + tan^2(A) = sec^2(A)
- cot^2(A) + 1 = cosec^2(A)

2. Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(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))

3. Double Angle Formulas:
- sin(2A) = 2sin(A)cos(A)
- cos(2A) = cos^2(A) - sin^2(A)
- tan(2A) = (2tan(A))/(1 - tan^2(A))

4. Half Angle Formulas:
- sin(A/2)

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