Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics

Solving these questions can yield great benefits. Ideally, try to attempt all the Class 10 Mathematics Selina Concise questions first by your own. If you can't, then refer to ICSE Class 10 Mathematics Selina Concise Chapter-wise solutions offered by Vedantu. Rather than mugging up the Mathematics questions, it is essential to understand the concept and enhance your problem- solving skill. The solutions provided are just for reference.

Trigonometric Identities are equalities involving trigonometry functions that hold for all values of the variables in the equation.

There are several different trigonometric identities that involve the side length and angle of a triangle. Only the right-angle triangle is subject to the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are the mathematical terms for sine, cosine, tangent, cosecant, secant, and cotangent. The sides of the right triangle, such as the adjacent, opposing, and hypotenuse sides, are used to define all of these trigonometric ratios. You can learn more about trigonometric identities from Trigonometrical Identities Solutions for ICSE Board Class 10 Mathematics.

Proving a trigonometric identity entails demonstrating that the identity holds regardless of the value of xx or theta employed.

We cannot just substitute in a few xx numbers to "prove" that they're equal because it has to hold true for all values of xx. It's possible that both sides are equal at numerous points (for example, when solving the equation), leading us to believe we have a true identity.

Instead, we must employ logical procedures to demonstrate that one side of the equation may be changed into the other. We'll sometimes work on each side separately until they meet in the middle.

Different trigonometric identities, such as reciprocal trigonometric functions and Pythagorean identities, should be recognisable to you.

There are numerous methods for proving one's identification. If you get stuck, here are some pointers:

1) Focus on the more difficult side of the equation. Try to make it as simple as possible.

2) If possible, replace all trigonometric functions with sin theta and cos theta.

3) Recognize algebraic operations such as factoring, expanding, applying the distributive property, and multiplying and adding fractions. This allows us to further reduce the phrase.

4) Make use of the different trigonometric identities. Keep an eye out for the Pythagorean identity in particular.

5) Collaborate on all sides.

6) Keep an eye on the opposite side of the equation and work toward it.

7) Take into account the "trigonometric conjugate."

Complementary angles are a pair of two angles whose sum equals 90 degrees. (90 - ) is the complement of an angle. Complementary angle trigonometric ratios are as follows:

• sin (90°- θ) = cos θ

• cos (90°- θ) = sin θ

• cosec (90°- θ) = sec θ

• sec (90°- θ) = cosec θ

• tan (90°- θ) = cot θ

• cot (90°- θ) = tan θ

The supplementary angles are a pair of two angles whose sum equals 180 degrees. An angle's supplement is equal to (180 -). Supplementary angle trigonometric ratios are as follows:

• sin (180°- θ) = sinθ

• cos (180°- θ) = -cos θ

• cosec (180°- θ) = cosec θ

• sec (180°- θ)= -sec θ

• tan (180°- θ) = -tan θ

• cot (180°- θ) = -cot θ

To prepare for trigonometric identities, it is imperative for students to learn the fundamentals of trigonometry completely. The foundation needs to be strong for building the knowledge further. Students must make sure that they remember the formulas. Without learning the formulas, students will not be able to solve problems related to trigonometric identities. To consolidate their knowledge further, students should solve sample papers and questions related to trigonometric identities. Students can find free study materials and sample papers on the Vedantu app and website.