Find the general solution of the equation sec2 2x = 1 – tan 2x

Asked by Pragya Singh | 1 year ago |  127

##### Solution :-

It is given that

sec2 2x = 1 – tan 2x

We can write it as

1 + tan2 2x = 1 – tan 2x

tan2 2x + tan 2x = 0

Taking common terms

tan 2x (tan 2x + 1) = 0

Here

tan 2x = 0 or tan 2x + 1 = 0

If tan 2x = 0

tan 2x = tan 0

We get

2x = nπ + 0, where n ∈ Z

x =$$\dfrac{n\pi}{2}$$, where n ∈ Z

tan 2x + 1 = 0

We can write it as

tan 2x = – 1

So we get

$$- tan\dfrac{\pi}{4}= tan(\pi-\dfrac{\pi}{4})$$

Here

2x = nπ + $$\dfrac{3\pi}{4}$$, where n ∈ Z

x = $$\dfrac{n\pi}{2}+ \dfrac{3\pi}{8}$$  , where n ∈ Z

Hence, the general solution is $$\dfrac{n\pi}{2}$$or $$\dfrac{n\pi}{2}$$ +$$\dfrac{3\pi}{8}$$, n ∈ Z.

Answered by Abhisek | 1 year ago

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