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Trigonometry Formula Sheet 2025: Essential Formulas for Classes 10 & 12

Trigonometry Formula Sheet 2025: Essential Formulas for Classes 10 & 12

Edited By Vishal kumar | Updated on Jan 28, 2025 02:37 PM IST

Trigonometry is one of the foundational branches of mathematics, playing very important role in everything from geometry to physics and engineering. Whether you're a student preparing for board exams or competitive exams like JEE Main, NEET or other state engineering this trigonometry formula sheet will be very useful for exam preparation. Having a comprehensive formula sheet at your fingertips can save time and simplify complex calculations.

This Story also Contains
  1. Types of Trigonometric Functions
  2. Trigonometric Identities-1 (Reciprocal ,Pythagorean ,Co-function and Even-Odd Identities)
  3. Trigonometric Identities-2 ( Double angled,half angled and Triple angled formulas)
  4. Trigonometric Identities-3 (Sum and difference identities, Sum-to-Product and Product-to-Sum Formulas)
  5. Trigonometric Ratios of Allied Angles
Trigonometry Formula Sheet 2025: Essential Formulas for Classes 10 & 12
Trigonometry Formula Sheet 2025: Essential Formulas for Classes 10 & 12

Understanding and memorizing these trigonometric formulas is crucial for students in Classes 10, 11, and 12, as they form the foundation for advanced mathematics and competitive exams. This comprehensive guide also includes a trigonometric table and inverse trigonometric formulas to help students tackle problems with ease and confidence which will help to boost your exam preparation journey.

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Types of Trigonometric Functions

Types of trigonemetric function

sinθ= Perpendicular  Hypotenuse =BCACcosθ= Base  Hypotenuse =ABACtanθ= Perpendicular  Base =BCABcosec=1sinθsec=1cosθcot=cosθsinθ=1tanθ

The above circle is the standard unit circle (centre at the origin and radius is equal to 1 unit)

sinθ=xr=x1=1cosθ=yr=y1=1

For a standard unit circle, the value of x and y give us the values of cosθ and sinθ respectively.

Trigonometric Function

Graphs of trigonometric functions:

Graphs of trigonometric functions:

Trigonometric Identities-1 (Reciprocal ,Pythagorean ,Co-function and Even-Odd Identities)

Trigonometric Identities:-

  • Reciprocal Identities

cscθ=1sinθsecθ=1cosθcotθ=1tanθ

  • Pythagorean Identities

sin2θ+cos2θ=1sec2θ=1+tan2θcsc2θ=1+cot2θ

  • Co-function Identities

cos(π2θ)=sinθsin(π2θ)=cosθcot(π2θ)=tanθtan(π2θ)=cotθcsc(π2θ)=secθsec(π2θ)=cscθ

  • Even-Odd Identities

sin(θ)=sinθcos(θ)=cosθtan(θ)=tanθcsc(θ)=cscθsec(θ)=secθcot(θ)=cotθ

Trigonometric Identities-2 ( Double angled,half angled and Triple angled formulas)

Trigonometric Identities:-

  • Double angled formulas

sin2θ=2sinθcosθcos2θ=cos2θsin2θ=2cos2θ1=12sin2θtan2θ=2tanθ1tan2θ

  • Half angled formulas

sin(θ2)=±1cosθ2cos(θ2)=±1+cosθ2tan(θ2)=1cosθsinθ

  • Triple angled identities

sin3x=3sinx4sin3xcos3x=4cos3x3cosxtan3x=3tanxtan3x13tan2x

Trigonometric Identities-3 (Sum and difference identities, Sum-to-Product and Product-to-Sum Formulas)

Trigonometric Identities:-

  • Sum and difference identities

sin(x+y)=sinxcosy+cosxsinysin(xy)=sinxcosycosxsinycos(x+y)=cosxcosysinxsinycos(xy)=cosxcosy+sinxsinytan(x+y)=tanx+tany1tanxtanytan(xy)=tanxtany1+tanxtany

  • Sum-to-Product Formulas

sinx+siny=2sin(x+y2)cos(xy2)sinxsiny=2cos(x+y2)sin(xy2)cosx+cosy=2cos(x+y2)cos(xy2)cosxcosy=2sin(x+y2)sin(xy2)

  • Product-to-Sum Formulas

sinxsiny=12[cos(xy)cos(x+y)]cosxcosy=12[cos(xy)+cos(x+y)]sinxcosy=12[sin(x+y)+sin(xy)]cosxsiny=12[sin(x+y)sin(xy)]

Trigonometric Ratios of Allied Angles

Trigonometric ratios of allied angles:

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