Question

Find the principal solutions of the casec X=2​

Answer 1

Given: cosec x=−2

⇒

sinx

1

=−2

⇒sinx=−

2

1

we know that sin30

o

=−

2

1

But we need negative value of sinx, sin is negative in III & IV quadrant.

Value in III quadrant =180

o

+30

o

=210

o

Value in IV quadrant =360

o

−30

o

=330

o

so principal solutions are

x=210

o

=

6

7π

x=330

o

=330

o

×

180

π

=

6

11π

General solution:

Let sinx=siny ..... (1)

sinx=−

2

1

......... (2)

from (1) & (2)

siny=−1/2

siny=sin

6

7π

⇒y=

6

7π

∴sinx=siny

General solution is

x=nπ+(−1)

n

y,n∈I

x=nπ+(−1)

n

(

6

7π

),n∈I