Question

find the principal of general solution if sec= -2​

Answer 1

Step-by-step explanation:

secx=2

We know, sec

3

π

=2 and sec

3

5π

=sec(2π−

3

π

)=sec

3

π

=2.

Therefore, the principal solutions are x=

3

π

and

3

5π

.

Now, secx=sec

3

π

cosx=cos

3

π

x=2nπ±

3

π

, where n∈Z.

Therefore, the general solution is x=2nπ±

3

π

,n∈Z

Answer 2

Given: sec= -2​.

To find: The principal of general solution if sec= -2​.

Solution: The principal and general solution of sec= -2​ is 2π/3 and 4π/3, and 2nπ±(2π/3).

We know that sec x is equal to -2. The secant of an angle is -2 when the angle is 120 degrees.

$sec x= sec 120$

       $= -2$

The secant of 120 can also be written as shown below.

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

Now, the secant of 120 can be written as shown below as well.

$sec ( \frac{2\pi }{3} ) =sec ( \frac{4\pi }{3} )$

            $=-2$

Thus, the principal solutions are

$x = \frac{2\pi }{3}$ and $\frac{4 \pi }{3}$

Now, since

$sec x = sec (\frac{2\pi }{3} )$

it can be written that

$cos x = cos (\frac{2\pi }{3} )$

Thus, the general solution is

$x = 2n\pi \frac{+}{} \frac{2\pi }{3}$, where n belongs to Z.

Therefore, the principal and general solution of sec= -2​ is 2π/3 and 4π/3, and 2nπ±(2π/3).