Standard Identities for Competitive Exams

The Quantitative Aptitude section of the SSC CGL exam can seem daunting to many aspirants. In particular, the topic of Standard Identities involves fundamental yet complex trigonometric equations that may initially mystify candidates.

However, developing a strong grasp of Standard Identities is crucial for maximizing one's score. This guide will demystify these identities, explain their significance, and provide tips to master them.

What Are Standard Identities?

Standard Identities refer to core trigonometric equations involving functions like sine, cosine, tangent, and their relationships. Some examples include:

Pythagorean Identities sin2(x) + cos2(x) = 1
sin2(x) = 1 - cos2(x)
tan2(x) = sin2(x)/cos2(x)
Sum Identities sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Double Angle Identities sin(2x) = 2sin(x)cos(x)
cos(2x) = cos2(x) - sin2(x)

Significance of Standard Identities

Conquering Standard Identities provides three key advantages:

  • Enables faster problem-solving by streamlining trigonometric manipulations
  • Strengthens overall understanding of trigonometric concepts and relationships
  • Minimizes errors thereby improving accuracy

Tips to Master Standard Identities

Here are some useful tips to master Standard Identities:

  • Memorize key identities through repetition
  • Practice extensively to reinforce understanding
  • Leverage online resources for clarity on concepts
  • Focus on understanding over rote memorization


By dedicating time and effort to understand and internalize Standard Identities, SSC CGL aspirants can unlock invaluable skills for acing the Quantitative Aptitude section. These identities may seem intimidating initially but are ultimately empowering tools on the path to exam success.


Q1: How many key Standard Identities are there?

A1: There are 5-6 fundamental Standard Identities including Pythagorean, Sum & Difference, Double Angle, Product-Sum & Sum-Product identities.

Q2: Is memorizing Standard Identities sufficient?

A2: No, memorization alone is not enough. One must practice extensively to reinforce understanding of how to apply these identities to problems.

Q3: Do we need to know proofs of Standard Identities?

A3: No, the SSC CGL syllabus does not require candidates to know proofs, only application in problem-solving.

Q4: Can online resources help in learning?

A4: Yes, there are many useful online resources like videos and articles explaining Standard Identities. These can supplement your preparation.

Q5: Are there tricks to remember these identities?

A5: Mnemonic devices and acronyms can help with memorization. Also linking identities to common trigonometric ratios is a useful trick.

Q6: How much time should one devote to this topic?

A6: At least 2-3 hours daily for a couple of weeks is advisable to develop fluency in applying Standard Identities.