Trigonometry Formulas for Quantitative Section in Competitive Exams

3 minute read
Trigonometry Formulas

Competitive exams have now become an essential element of the current education system in India as most of the leading universities rely on them for selecting candidates across courses. Due to the increase in the number of applicants, varsities across India consider scores of competitive exams to test the proficiency and shortlist the potential candidates. Apart from competitive exams for educational entries, there are several exams through which the candidates can attain their dream job like SSC CGL, various bank exams etc. Majorly such exams gauge the calibre of candidates on the parameters like Reasoning and Logical Abilities, Language Proficiency and Quantitative Reasoning Section. Generally, aspirants find it comparatively tougher to prepare and score well in the quant section because of the intricate and complex topics like Trignometry. If you are also planning to appear for one such examination, here is a blog to help you with some trigonometry formulas. 

List of Trigonometry Formulas

Let’s have a look at the specific angle value-based trigonometry formulas:  

θ 30° 45° 60° 90° 180°
Sin  0 1/2 1/2 3/2 1 0
Cos  1 3/2 1/2 1/2 0 -1
Tan   0 1/3 1 3 0
Cot  3 1 1/3 0
Sec  1 2/3 2 2 -1
Cosec  2 2 2/3 1

Here are some essential trigonometric formulas and identities:

  • Sinθ= 1/ Cosecθ or Sin θ.Cosecθ= 1
  • Cosθ= 1/Secθ or Cos θ.Secθ= 1
  • Tanθ= 1/Cotθ or Tanθ.Cotθ= 1
  • 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)

Basic Trigonometry Identities 

Tangent & Cotangent 

  • Tanθ = Sinθ/cosθ
  • Cotθ = Cosθ/Sinθ


  • Sinθ = 1/Cosecθ
  • Cosecθ= 1/Sinθ
  • Cosθ= 1/Secθ
  • Secθ = 1/Cosθ
  • Tanθ = 1/Cotθ
  • Cotθ = 1/Tanθ


  • Sin^2θ + Cos^2θ = 1
  • 1+ Tan^2θ = Sec^2θ
  • 1+ Cot^2θ = Cosec^2

Even Odd

  • Sin (-θ) = -Sinθ
  • Cos (-θ) = Cosθ
  • Sec (-θ) = Secθ
  • Cosec (-θ) = – Cosecθ
  • Tan (-θ) = Cotθ
  • Cot (-θ) = Tanθ

Solved Examples

Learning via solved examples is easier than just going through mere formulas. hence, for a better understanding of the above mentioned and some other trigonometry formulas. Leverage Edu has provided a series of such examples below:

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List of Practice Questions

On the above understanding of your trigonometric formulas, here are some questions for you to practice and qualify the exam with flying colours.

Tips and Tricks To Ace Trigonometry Formulas and Questions 

While preparing for the competitive exams it is essential to adopt the principle of hard work vs smart work. Regular practice before the exam can be your success mantra to outshine with your marks. Below mentioned are some of the essential tips which you can incorporate in practising schedule and get a better hold of the topic:

  • Must of us struggle with the trigonometric identity questions where we have to prove that the LHS is equal to the RHS, in such questions the smarter approach is to start the question from the complex side. As it is easier to eliminate and induce the answer. 
  • Try converting the tan, sec, cosec, cot functions into sin and cosine function so that you will be able to use the standardized trigonometry formulas. 
  • It would be beneficial to convert the terms into single fractions and reduce them to the fullest. 
  • Use Pythagorean Identities to convert the functions with square into normal terms. Now you can apply the usual trigonometric formulas. 
  • Rather than just sticking to the set identities, you must try to apprehend the use of simple procedures like expansion, factorization, simplification and cancellation.  

Reference Books for Trignometry 

Apart from taking up coaching for competitive exams, one can ace the quantitative section by practising on their own from reference and practise books. Considering the importance of these books, we have picked the best ones for you to ace this particular section: 

Book Links
PLANE TRIGONOMETRY Part-1 by SL Loney Buy Here.
Understand Trigonometry: A Teach Yourself Guide by Paul Abbott Buy Here.
Sneaky Math: A Graphic Primer with Projects by CY Tymony Buy Here.
E-Z Trigonometry  Buy Here.
Learn or Review Trigonometry: Essential Skills by Chris McMullen Buy Here.

This was all about trigonometry formulas for competitive exam, we have provided you with most of the important formulas to begin your preparation. We all know that trigonometry is an essential part of the quantitative section which is a part of the important exams like GRE Mathematics and some likely competitive exams. Contact us at Leverage Edu, to know more about the top-notch institutes for GRE and competitive exam preparations.  

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