Answer

Verified

476.1k+ views

Hint: In this question use the property of tan$\theta $ which is $\tan \theta = \cot \left( {{{90}^0} - \theta } \right)$, $\dfrac{1}{{\tan x}} = \cot x$, so use these properties of tan$\theta $ to reach the solution of the question.

Complete step-by-step answer:

Given equation is

$\tan \theta \tan {40^0} = 1$

$ \Rightarrow \tan \theta = \dfrac{1}{{\tan {{40}^0}}}$

Now as we know that $\dfrac{1}{{\tan x}} = \cot x$, so use this property in above equation we have,

$ \Rightarrow \tan \theta = \dfrac{1}{{\tan {{40}^0}}} = \cot {40^0}$

$ \Rightarrow \tan \theta = \cot {40^0}$

Now as we know that $\tan \theta = \cot \left( {{{90}^0} - \theta } \right)$, so substitute this value in above equation we have,

$ \Rightarrow \cot \left( {{{90}^0} - \theta } \right) = \cot {40^0}$

So, on comparing we have,

$\begin{gathered}

{90^0} - \theta = {40^0} \\

\Rightarrow \theta = {90^0} - {40^0} = {50^0} \\

\end{gathered} $

So, this is the required value of $\theta $.

Note: In such types of questions the key concept we have to remember is that we always recall all the basic trigonometric properties which are stated above, then using these properties simplify the given equation, we will get the required value of $\theta $.

Complete step-by-step answer:

Given equation is

$\tan \theta \tan {40^0} = 1$

$ \Rightarrow \tan \theta = \dfrac{1}{{\tan {{40}^0}}}$

Now as we know that $\dfrac{1}{{\tan x}} = \cot x$, so use this property in above equation we have,

$ \Rightarrow \tan \theta = \dfrac{1}{{\tan {{40}^0}}} = \cot {40^0}$

$ \Rightarrow \tan \theta = \cot {40^0}$

Now as we know that $\tan \theta = \cot \left( {{{90}^0} - \theta } \right)$, so substitute this value in above equation we have,

$ \Rightarrow \cot \left( {{{90}^0} - \theta } \right) = \cot {40^0}$

So, on comparing we have,

$\begin{gathered}

{90^0} - \theta = {40^0} \\

\Rightarrow \theta = {90^0} - {40^0} = {50^0} \\

\end{gathered} $

So, this is the required value of $\theta $.

Note: In such types of questions the key concept we have to remember is that we always recall all the basic trigonometric properties which are stated above, then using these properties simplify the given equation, we will get the required value of $\theta $.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE