Question

If cos a = root 3 divided by 2 then the value of (cosec^2 a - sec^2 a) divided by (cosec^2 a + sec^2 a) is

Answer 1

Step-by-step explanation:

The value of \frac{1-sec\theta}{1+cosec\theta}

1+cosecθ

1−secθ

= \frac{3-2\sqrt{3}}{9}

9

3−2

3

.

The value of cosθ = √3/2.

Now using the identity, sin²θ + cos²θ = 1

sin²θ = 1 - (3/4)

sin²θ = 1/4

sinθ = (1/2)

Now, we have to find the value of \frac{1-sec\theta}{1+cosec\theta}

1+cosecθ

1−secθ

.

Substituting the values in the given expression , we get

\frac{1-sec\theta}{1+cosec\theta}

1+cosecθ

1−secθ

= \frac{1-(1/cos\theta)}{1+(1/sin\theta)}

1+(1/sinθ)

1−(1/cosθ)

= \frac{1-2/(\sqrt{3})}{1+(2)}

1+(2)

1−2/(

3

)

= \frac{(\sqrt{3})-2}{3(\sqrt{3})}

3(

3

)

(

3

)−2

= \frac{3-2\sqrt{3}}{9}

9

3−2

3