Question

If cos theta=a/b then find cosec theta

Answer 1

Answer:

The required answer is $\frac{p}{\sqrt{h^{2}-p^{2}}}$

Step-by-step explanation:

Cos theta=The ratio of the neighboring side to the hypotenuse is known as the Cos theta or Cos, where is one of the acute angles.

Cosec theta: the angle's opposite side's length divided by the hypotenuse's length.

Given:  cos theta$=a/b$

To find: the value of cosec theta.

Solution:

We know that cos θ$=b/h=a/b$

So, value of b=a, h=p, p=?

According to Pythagoras theorem.

In △ ABC

$h^{2}=p^{2}+b^{2}\\h^{2}-b^{2}=p^{2}$

or

$p=\sqrt{h^{2}-b^{2}}$

Cosec=$\frac{h}{p}=\frac{p}{\sqrt{h^{2}-p^{2}}}$

Hence, the value of cosec theta is $\frac{p}{\sqrt{h^{2}-p^{2}}}$

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