Question

if cos theta is equals to 1 by root 3 then what is the value of 1 by tan square theta​

Answer 1

the correct answer is 1/tan²∅ = 1/2

for further explanation pls refer the image

hope this helps...

Answer 2

Main concept

In this trigonometric problem, we can use two different methods:

1. By using trigonometric identity
2. By using trigonometric ratio

Let's use trigonometric identity method, since its easier to understand and solve the problem.

Identities and Ratios

In this problem, we are going to use important formulas. They are:

$\Rightarrow{\tt{cos^2 \theta = \dfrac{1}{sec^2 \theta}}}$

$\Rightarrow{\tt{tan^2 \theta = sec^2 \theta - 1}}$

Solution

First let's square the value of $\tt{cos \theta}$. We have,

$\Rightarrow{\tt{cos \theta = \dfrac{1}{\sqrt{3}}}}$

$\Rightarrow{\tt{cos^2 \theta = \dfrac{1}{3}}}$

We know that,

$\Rightarrow{\tt{cos^2 \theta = \dfrac{1}{sec^2 \theta}}}$

$\Rightarrow{\tt{\dfrac{1}{3} = \dfrac{1}{sec^2 \theta}}}$

$\Rightarrow{\tt{sec^2 \theta = 3}}$

Now, on using identity, we get:

$\Rightarrow{\tt{tan^2 \theta = sec^2 \theta - 1}}$

$\Rightarrow{\tt{tan^2 \theta = 3 - 1}}$

$\Rightarrow{\tt{tan^2 \theta = 2}}$

According to the question, we need to find $\tt{\dfrac{1}{tan^2 \theta}}$

$\Rightarrow{\boxed{\tt{\dfrac{1}{tan^2 \theta} = \dfrac{1}{2}}}}$

Hence, this is the required answer.