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Trigonometric Functions of Sum & Difference of Two Angles Video Lecture | Mathematics (Maths) for JEE Main & Advanced

Name: Trigonometric Functions of Sum & Difference of Two Angles Video Lecture | Mathematics (Maths) for JEE Main & Advanced
Uploaded: 2019-11-09T10:21:39Z
Description: Video Lecture & Questions for Trigonometric Functions of Sum & Difference of Two Angles Video Lecture | Mathematics (Maths) for JEE Main & Advanced - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) for JEE Main & Advanced.

FAQs on Trigonometric Functions of Sum & Difference of Two Angles Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What are the formulas for the sine and cosine of the sum and difference of two angles?

Ans. The formulas for the sine and cosine of the sum and difference of two angles \(A\) and \(B\) are as follows: - Sine of sum: \(\sin(A + B) = \sin A \cos B + \cos A \sin B\) - Sine of difference: \(\sin(A - B) = \sin A \cos B - \cos A \sin B\) - Cosine of sum: \(\cos(A + B) = \cos A \cos B - \sin A \sin B\) - Cosine of difference: \(\cos(A - B) = \cos A \cos B + \sin A \sin B\).

2. How can the sum and difference formulas be used to simplify trigonometric expressions?

Ans. The sum and difference formulas can simplify trigonometric expressions by allowing us to break down complex angles into simpler components that can be calculated more easily. For example, to find \(\sin(75^\circ)\), we can express it as \(\sin(45^\circ + 30^\circ)\) and then apply the sine sum formula: \(\sin(75^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ\).

3. Can the sum and difference formulas be applied to angles in radians?

Ans. Yes, the sum and difference formulas can be applied to angles in radians just as they are with degrees. The formulas remain the same, and you can use them to calculate the sine and cosine of angles expressed in radians. For instance, for \(A = \frac{\pi}{4}\) and \(B = \frac{\pi}{6}\), you can use the same formulas to find \(\sin\left(\frac{\pi}{4} + \frac{\pi}{6}\right)\).

4. How do you derive the sum and difference formulas for sine and cosine?

Ans. The sum and difference formulas can be derived using geometric interpretations or the unit circle. For instance, one way to derive \(\sin(A + B)\) is to consider the coordinates of points on the unit circle corresponding to angles \(A\) and \(B\) and apply the Pythagorean theorem, which leads to the relationship between the sine and cosine of the combined angles.

5. Are there any specific examples of problems that can be solved using the sum and difference formulas?

Ans. Yes, specific examples include finding the exact values of trigonometric functions for angles that are not standard. For instance, to calculate \(\cos(75^\circ)\), you can express it as \(\cos(45^\circ + 30^\circ)\) and apply the cosine sum formula: \(\cos(75^\circ) = \cos(45^\circ)\cos(30^\circ) - \sin(45^\circ)\sin(30^\circ)\), which simplifies to a numerical value.

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Sep 20, 2025 Last updated

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	Mathematics (Maths) for JEE Main & Advanced 176 videos\|588 docs\|160 tests

Mathematics (Maths) for JEE Main & Advanced

176 videos|588 docs|160 tests

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