## Trigonometry Function Formulas

So, here are few Trigonometry Function Formulas. Let’s learn some basics of these formulas.

So, here are few Trigonometry Function Formulas. Let’s learn some basics of these formulas.

**Trigonometry Function Formulas of a Right Triangle :**

sin α = a / c = opposite / hypotenuse

cos α = b / c = adjacent / hypotenuse

tan α = a / b = opposite / adjacent

cot α = b / a = adjacent / opposite

sec α = c / b Cosec α = c / a

sin^{2} α + cos^{2} α = 1

tan α . cot tan α = 1

tan α = sin α / cos α = 1 / cot tan α

cot tan α = cos α / sin α = 1 / tan α

1 + tan^{2} α = 1 / cos^{2} α = sec^{2} α

1 + cot tan^{2} α = 1 / sin^{2} α = cos sec^{2} α

α | 0^{0} | 30^{0} | 45^{0} | 60^{0} | 90^{0} | 120^{0} | 180^{0} | 270^{0} | 360^{0} |

sin α | 0 | 1/2 | √2/2 | √3/2 | 1 | √3/2 | 0 | -1 | 0 |

cos α | 1 | √3/2 | √2/2 | 1/2 | 0 | -1/2 | -1 | 0 | 1 |

tan α | 0 | 1/√3 | 1 | √3 | ∞ | -√3 | 0 | ∞ | 0 |

cot α | ∞ | √3 | 1 | 1/√3 | 0 | -1/√3 | ∞ | 0 | ∞ |

sec α | 1 | 2/√3 | √2 | 2 | ∞ | -2 | -1 | ∞ | 1 |

cosec α | ∞ | 2 | √2 | 2/√3 | 1 | 2/√3 | ∞ | -1 | ∞ |

sin | cos | tan | cot | |

-α | -sin α | +cos α | -tan α | -cot α |

90^{0} – α | +cos α | +sin α | +cot α | +tan α |

90^{0} + α | +cos α | -sin α | -cot α | -tan α |

180^{0} – α | +sin α | -cos α | -tan α | -cot α |

180^{0} + α | -sin α | -cos α | +tan α | +cot α |

270^{0} – α | -cos α | -sin α | +cot α | +tan α |

270^{0} + α | -cos α | +sin α | -cot α | -tan α |

360^{0}k – α | -sin α | +cos α | -tan α | -cot α |

360^{0}k – α | +sin α | +cos α | +tan α | +cot α |

- sin(A + B) = sinA cosB + cosA sinB
- sin(A – B) = sinA cosB – cosA sinB

- cos(A + B) = cosA cosB – sinA sinB
- cos(A – B) = cosA cosB + sinA sinB

- tan (A + B) = tanA + tanB / 1 – tanA tanB
- tan(A – B) = tanA – tanB / 1 + tanA tanB

- cot (A+ B) = cotA cotB – 1 / cotA + cotB

- sin α cos β = 1/2 [ sin (α + β) + sin(α – β)]
- cos α sin β = 1/2 [ sin (α + β) – sin(α – β)]
- cos α cos β = 1/2 [ cos (α + β) + cos(α – β)]
- sin α sin β = 1/2 [ cos (α – β) – cos(α + β)]

- tan α tan β = tan α + tan β / cot tan α + cot tanβ = – tanα – tan β / cot tan α – cot tan β

Trigonometric Formula with t = tan(x/2)

sinx = 2t / 1 + t^{2}

cos x = 1 – t^{2} / 1 + t^{2}

tan x = 2t / 1 – t^{2}

cot x = 1 – t^{2} / 2t

- A, B, C are 3 angles of a triangle
- sin A + sin B + sin c = 4 cos(A / 2) cos(B/2) cos(C/2)
- cosA + cos B + cos C = 4 sin(A/2) sin(B/2) sin(C/2) + 1
- sinA + sinB – sinC = 4sin (A/2) sin (B/2) cos (C/2)

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This is good?????

Intellegent

Sir me mathematics ka silvers chAiye

Please let these formulaes in easy way ..

And don’t expand it so much..

if n is a natural number .which is the solution to the equation tan(5a)=cot(3a)?

a=alpha symbol

5a = 90 – 3a

2a = 90

a = 45, then use the TanA = TanB formula to get the answer…

a belongs to (n(pi) +-(pi/2))

Nice formulaes

i like it……….

Nice but some formulas missing .