__Introduction Trigonometric__-

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically. These calculations soon came to be defined as the trigonometric functions and today are pervasive in both pure and applied mathematics: fundamental methods of analysis such as the Fourier transform.

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__ Application__-

#### Pythagorean Theorem.

##### •__Statment of Pythagorean Theorem-__

Pythagorean Theorem states that; in a right-angled triangle the square of the hypotenuse longest side is equal to the sum of the squares of the other two sides.__According to Pythagorean Theorem-__

In Trangle ΔABC,( Hypotenuse)² = (Base)² + (Tanjent)²

(c)² = (b)² + (a)²

c = √(a)² + √(b)²

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• __Trigonometric identities-__

The following intities are related to the pyathagorean-

♦ sin²A+cos²A = 1

♦ tan²A+1 = sec²

♦ cot²+1 = cosec²

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• __Formula for the Sum/Defference of Two Angle -__

♦ sin(A±B) = sinA.cosB±cosA.sinB

♦ cos(A±B) = cosA.cosB±sinA.sinB

♦ tan(A±B) = (tanA±tanB)/1±tanA.tanB

♦ cot(A±B) = 1±cotA.cotB/cotA±B

♦ sin(A+B)sin(A-B) = sin²A-sin²B

♦ cos(A+B)cos(A-B) = cos²A-cos²B

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• __Formula of sin And cos of sumation And Sub-Traction -__

♦ 2sinA.cosB = sin(A+B)+sin(A-B)

♦ 2cosA.sinB = sin(A+B)-sin(A-B)

♦ 2cosA.cosB = cos(A+B)+cos(A-B)

♦ 2sinA.sinB = cos(A-B)+cos(A+B)

♦ sinC+sinD = 2cos(C+D)/2.cos(C-D)/2

♦ sinC-sinD = 2cos(C+D)/2.cos(C-D)/2

♦ cosC-cosD = 2sin(C+D)/2.sin(C-D)/2

♦ cosC+cosD = 2cos(C+D)/2.cos(C-D)/2

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• __Area of Trangle-__

Area = Δ = √s(s-a)(s-b)(s-b) = abc/4r