Question

If cot theta=9/40 pi greater than theta greater than 3pi/2,find the values of cosec theta , tan theta, sec theta , cos theta, sin theta​

Answer 1

Answer:

ANSWER

tanx=

4

3

π<x<3

2

π

180<x<

2

3

×180

=180<x<270

=90<

2

x

<

2

270

=

2

π

<

2

x

<

4

3π

⇒

2

x

lies in 2

nd

quadrant.

sin

2

x

is positive.

cos

2

x

is negative.

tan

2

x

is negative.

tanx=

4

3

tanx=

1−tan

2

2

x

2tan

2

x

=

4

3

=

1−tan

2

2

x

2tan

2

x

⇒3−3tan

2

2

x

=8tan

2

x

⇒3tan

2

2

x

+8tan

2

x

−3=0

⇒3tan

2

2

x

+9tan

2

x

−tan

2

x

−3=0

⇒3tan

2

x

(tan

2

x

+3)−1(tan

2

x

+3)=0

3tan

2

x

−1=0 & tan

2

x

+3=0

⇒3tan

2

x

=1 tan

2

x

=−3

⇒tan

2

x

=

3

1

(not possible as tan

2

x

is negative}

∴tan

2

x

=−3

Consider, cos

2

x

=

sec

2

x

1

=

1+tan

2

2

x

−1

=

1+(−3)

2

−1

=

10

−1

∴cos

2

x

=

10

−1

Consider,

sin

2

x

=tan

2

x

×cos

2

x

=(−3)(−1/

10

)

=

10

3

.