Understand The Trigonometric Identities

Many learners love to be entangled in mathematical problems. They have some strange fixation with mathematical tools and have a unique way with them. They involve themselves with the nuances of mathematics so much that they forget there’s a life beyond their mathematics textbooks. Their love for mathematics makes them opt for mathematics for higher studies and eventually engage in research too. On the contrary, some absolutely despise mathematics as a subject. The tools that aid in problem-solving end up baffling them. For some, the hate rises to a magnitude that they develop what is called maths phobia. The hate usually arises due to unclear mathematical rules and concepts, lack of enough practice, or maybe not so good mentoring.

Mathematics is a subject in which if a learner’s elementary concepts are clouded then even solving uncomplicated problems can be nerve-racking. Which leads to frustration and generates aversion towards the subject. Therefore, learners must understand that besides focusing on problem-solving one must also engage with elemental concepts.

Through our article on trigonometric identities, we have tried to explain the concepts behind the same to enable our readers to have fun with one of the most interesting topics in mathematics are called Trigonometry. Make sure to read the article thoroughly to be able to adequately use trigonometric tools for solving various trigonometry questions in exams.

What Are Trigonometric Identities & Their Applications?

Trigonometric identities are the equalities that are applied in trigonometric functions. They stand true to every value of the variables occurring on both sides of the equality are defined. The trigonometric identities are used to solve all types of trigonometric problems. They can be used in formulas, complex trigonometric questions to solve them quickly. Let us see all the fundamental trigonometric identities here. Whenever there is a need to simplify the expressions that involve trigonometric functions, the knowledge of trigonometric identities comes very handy. One of the most important applications of trigonometric identities is the integration of non-functional trigonometric functions.

To understand the application of trigonometric identities one can examine one of the most common procedures wherein, a learner first uses the substitution method with trigonometric functions and then simplifies the consequent integral using the trigonometric identities.

How Many Fundamental Trigonometric Identities Are Used?

Different types of trigonometric identities involve the side length along with the angle of a triangle. Learners must keep in mind that the trigonometric identities hold only in the cases of the right-angled triangles. All the known trigonometric identities are based on a total of six trigonometric ratios namely, sine, cosine, tangent, cosecant, secant, and cotangent. We will name the fundamental trigonometric identities below. Make sure to check all of them one by one.

  1. Ratio Trigonometric Identities
  2. Triple Trigonometric Identities
  3. Negative Trigonometric Identities
  4. Products Trigonometric Identities
  5. Quotients Trigonometric Identities
  6. Reciprocal Trigonometric Identities
  7. Even Odd Trigonometric Identities
  8. CoFunction Trigonometric Identities
  9. Pythagorean Trigonometric Identities
  10. Double Angle Trigonometric Identities
  11. Product & Sum Trigonometric Identities
  12. Opposite Angled Trigonometric Identities
  13. Supplementary Angle Trigonometric Identities
  14. Complementary Angles Trigonometric Identities
  15. Half Angle Trigonometric Identities or Power Reducing Formulas
  16. Sum & Difference of Angles Trigonometric Identities of Bhaskaracharya

Furthermore, find out what are trigonometric ratios, related formulas, functions, and types.

Now, let’s see the seven basic trigonometric identities, these are the most commonly used while solving complex trigonometric identities. You need to memorize the following trigonometric identities to be able to do well in trigonometric and geometric questions.

  1. Sec θ = 1/Cos θ
  2. Cot θ = 1/Tan θ
  3. Cosec θ = 1/Sin θ
  4. Tan θ = Sin θ/Cos θ
  5. Cot θ = Cos θ/Sin θ
  6. Sin2θ + Cos2 θ = 1
  7. 1 + tan2 θ = sec2 θ

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