Question

$3 \sin ^{2} x+2 \sin x \cos x=2$

Name: Problem 58, Chapter 12: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-08-23T08:47:06-08:00
Duration: 1 min 41 s
Channel: Aman Gupta
Description: 3 sin^2 x+2 sinx cosx=2

   $3 \sin ^{2} x+2 \sin x \cos x=2$

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Sanjiva Dayal IIT… 1st Edition

Chapter 12, Problem 58

Instant Answer

Solved by Expert Aman Gupta

08/23/2021

Step 1

We can rewrite this equation as $3 \sin ^{2} x+ \sin 2x =2$. Show more…

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$3 \sin ^{2} x+2 \sin x \cos x=2$

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Key Concepts

Trigonometric Identities

These are formulas that relate trigonometric functions to one another, such as the Pythagorean identity, double-angle formulas, and sum-to-product formulas. They are essential for rewriting and simplifying trigonometric expressions, which is a critical step in solving trigonometric equations.

Double-Angle Formulas

These formulas express trigonometric functions of double angles in terms of single angles, for example, rewriting a product like 2 sin(x) cos(x) as sin(2x). This transformation simplifies complex expressions and plays a crucial role in solving equations involving multiple trigonometric terms.

Solving Trigonometric Equations

This concept involves finding all angle measures that satisfy a given trigonometric equation. It requires techniques such as applying relevant trigonometric identities, manipulating and simplifying expressions, and accounting for the periodic nature of trigonometric functions to capture all possible solutions.

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