Find the principal and general solutions of the equation secx=2

Asked by Pragya Singh | 1 year ago |  58

##### Solution :-

Here it is given that,

secx=2

Now we know that

$$sec= \dfrac{\pi}{3}=2$$ and

$$sec\dfrac{5\pi}{3}=sec(2\pi- \dfrac{\pi}{3})$$

$$sec\dfrac{\pi}{3}=2$$

Therefore, the principal solutions are

$$\dfrac{\pi}{3}$$ and $$\dfrac{5\pi}{3}$$

Now, $$secx=sec \dfrac{\pi}{3}$$

and we know ,

$$secx=\dfrac{1}{cosx}$$

Therefore , we have,

$$cosx=cos \dfrac{\pi}{3}$$

Which implies,

$$x=2nπ\pm \dfrac{\pi}{3},n\in Z$$

Answered by Abhisek | 1 year ago

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