step 1 In this problem, the given equation can be rewritten as 3 into sine 2x is 2 sine x cos of x plus

3 sin2 x+cos2 x=2

Name: Problem 89, Chapter 12: Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry
Uploaded: 2021-08-23T11:36:16-08:00
Duration: 1 min 44 s
Channel: Aman Gupta
Description: 3 sin2 x+cos2 x=2

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Key Concepts

Amplitude-Phase Transformation

This method allows one to combine multiple trigonometric terms into a single sine or cosine function. It involves calculating R, the amplitude, as the square root of the sum of the squares of the coefficients, and ?, the phase angle, through an appropriate inverse trigonometric function. This transformation simplifies solving the equation by reducing it to a standard form.

Trigonometric Equations

These are equations that involve trigonometric functions of a variable. Solving them usually requires the use of trigonometric identities, understanding periodic properties, and manipulating expressions to simplify the equation to a form that can be solved for the variable.

Linear Combination of Sine and Cosine

A common technique in trigonometry involves expressing a linear combination of sine and cosine functions as a single sinusoid. This is done by finding an amplitude and a phase shift such that A sin? + B cos? is rewritten as R sin(? + ?), where R is the amplitude and ? is the phase shift.

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