Find the general solution for each of the following equation: sin x + sin 3x + sin 5x = 0 - Noon Academy

Find the general solution for each of the following equation: sin x + sin 3x + sin 5x = 0

Class 11 | Exercise 3.4 | Maths | NCERT | Trigonometric Functions

Find the general solution for each of the following equation: sin x + sin 3x + sin 5x = 0

GIVEN:

$sin\text{ }x\text{ }+\text{ }sin\text{ }3x\text{ }+\text{ }sin\text{ }5x\text{ }=\text{ }0$

OR,

$\left( sin\text{ }x\text{ }+\text{ }sin\text{ }5x \right)\text{ }+\text{ }sin\text{ }3x\text{ }=\text{ }0$

BY FORMULA,

NCERT Solutions for Class 11 Chapter 3 Ex 3.4 Image 12

OR,

$2\text{ }sin\text{ }3x\text{ }cos\text{ }\left( -\text{ }2x \right)\text{ }+\text{ }sin\text{ }3x\text{ }=\text{ }0$

OR,

$2\text{ }sin\text{ }3x\text{ }cos\text{ }2x\text{ }+\text{ }sin\text{ }3x\text{ }=\text{ }0$

COMMON TERMS ARE TAKEN OUT

NOW,

$sin\text{ }3x\text{ }\left( 2\text{ }cos\text{ }2x\text{ }+\text{ }1 \right)\text{ }=\text{ }0$

Here

$sin\text{ }3x\text{ }=\text{ }0\text{ }or\text{ }2\text{ }cos\text{ }2x\text{ }+\text{ }1\text{ }=\text{ }0$

In the event that wrongdoing

$3x\text{ }=\text{ }0$

$3x\text{ }=\text{ }n\pi ,\text{ }where\text{ }n\in Z$

We get

$x\text{ }=\text{ }n\pi /3,\text{ }where\text{ }n\in Z$

In the event that

$2\text{ }cos\text{ }2x\text{ }+\text{ }1\text{ }=\text{ }0$

$cos\text{ }2x\text{ }=\text{ }\text{ }1/2$

By additional rearrangements

$=\text{ }\text{ }cos\text{ }\pi /3$

$=\text{ }cos\text{ }\left( \pi \text{ }\text{ }\pi /3 \right)$

So we get

$cos\text{ }2x\text{ }=\text{ }cos\text{ }2\pi /3$

Here

NCERT Solutions for Class 11 Chapter 3 Ex 3.4 Image 13

i

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