Question

if sin theta*sec theta =-1& theta lies in 2nd quadrant find sin theta and sec theta​

Answer 1

Answer:

ANSWER

Given: sinθsecθ=−1

⇒sinθ×

cosθ

1

=−1

⇒sin

2

θ=cos

2

θ

⇒sin

2

θ=1−sin

2

θ

⇒sin

2

θ=

2

1

⇒sinθ=±

2

1

As θ lies in second quadrant ;

⇒θ=

4

3π

⇒sinθ=sin

4

3π

=

2

1

⇒secθ=sec

4

3π

=−

2

Answer 2

Given : sinθsecθ= -1   and θ lies in the second quadrant

To Find : sinθ and  secθ

Solution:

sinθsecθ= -1

=> sinθ/cosθ= -1

=> tanθ= -1

=> θ = 135° as  θ lies in the second quadrant

Sin 135°  = 1/√2

cos 135°  = -1/√2

=> sec  135°  = - √2

sinθ  = 1/√2 and  secθ =  - √2

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