Find the general solution for each of the following equation: sec2 2x = 1 – tan 2x - Noon Academy

Find the general solution for each of the following equation: sec2 2x = 1 – tan 2x

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

Find the general solution for each of the following equation: sec2 2x = 1 – tan 2x

GIVEN:

$sec2\text{ }2x\text{ }=\text{ }1\text{ }\text{ }tan\text{ }2x$

OR,

$1\text{ }+\text{ }tan2\text{ }2x\text{ }=\text{ }1\text{ }\text{ }tan\text{ }2x$

$tan2\text{ }2x\text{ }+\text{ }tan\text{ }2x\text{ }=\text{ }0$

COMMON TERMS ARE TAKEN,

$tan\text{ }2x\text{ }\left( tan\text{ }2x\text{ }+\text{ }1 \right)\text{ }=\text{ }0$

Here ,

$tan\text{ }2x\text{ }=\text{ }0\text{ }or\text{ }tan\text{ }2x\text{ }+\text{ }1\text{ }=\text{ }0$

On the off chance that

$tan\text{ }2x\text{ }=\text{ }0$

$tan\text{ }2x\text{ }=\text{ }tan\text{ }0$

We get

$2x\text{ }=\text{ }n\pi \text{ }+\text{ }0,\text{ }where\text{ }n\in Z$

$x\text{ }=\text{ }n\pi /2,\text{ }where\text{ }n\in Z$

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

We can compose it as

$tan\text{ }2x\text{ }=\text{ }\text{ }1$

So we get

NCERT Solutions for Class 11 Chapter 3 Ex 3.4 Image 11

NOW,

$2x\text{ }=\text{ }n\pi \text{ }+\text{ }3\pi /4,\text{ }where\text{ }n\in Z$

$x\text{ }=\text{ }n\pi /2\text{ }+\text{ }3\pi /8,\text{ }where\text{ }n\in Z$

Subsequently, the overall arrangement is

$n\pi /2\text{ }or\text{ }n\pi /2\text{ }+\text{ }3\pi /8,\text{ }n\in Z.$

i

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