# Find the value of $\dfrac{{\tan {{70}^0} - \tan {{20}^0}}}{{\tan {{50}^0}}}$ from the options given below

A. 2

B. 1

C. 0

D. 3

Last updated date: 17th Mar 2023

•

Total views: 304.5k

•

Views today: 2.87k

Answer

Verified

304.5k+ views

Hint: Make use of the formula of tan(x-y) and express the numerator in a solvable form using this formula and solve it.

Complete step-by-step answer:

We have been asked to find out the value of $\dfrac{{\tan {{70}^0} - \tan {{20}^0}}}{{\tan {{50}^0}}}$

So, now we will make use of the formula

$\tan (x - y) = \dfrac{{\tan x - \tan y}}{{1 + \tan x\tan y}}$

So, from this we get tanx-tany=tan(x-y)(1+tanxtany)

So, let us express the numerator in this from, so we get

$\dfrac{{\tan ({{70}^0} - {{20}^0})(1 + \tan {{70}^0}.\tan {{20}^0})}}{{\tan {{50}^0}}}$

Now, in the denominator,

$\tan {50^ \circ } = \tan ({70^ \circ } - {20^ \circ })$

So, we can write the expression as

$\dfrac{{\tan ({{70}^ \circ } - {{20}^ \circ })(1 + \tan {{70}^ \circ }.\tan {{20}^ \circ })}}{{\tan ({{70}^ \circ } - {{20}^ \circ })}}$

So, from this,

$\tan ({70^ \circ } - {20^ \circ })$ in the numerator and denominator would get cancelled out

So, we get the equation as:

$(1 + \tan {70^ \circ }\tan {20^ \circ })$

Now, this can be further written as \[(1 + \tan ({90^ \circ } - {20^ \circ })\tan {20^ \circ })\]

We , also know the result which says $\tan ({90^ \circ } - \theta ) = \cot \theta $

So, from this we get $1 + \cot {20^ \circ }\tan {20^ \circ }$

Since, cot and tan are reciprocal of each other,

We can write $1 + \dfrac{1}{{\tan {{20}^ \circ }}} \times \tan {20^ \circ }$

=1+1=2

So, from this, we can write $\dfrac{{\tan {{70}^0} - \tan {{20}^0}}}{{\tan {{50}^0}}} = 2$

So, option A is the correct answer for this question

Note: Make use of the appropriate trigonometric formula which is needed and then from that obtain the needed result , also make sure to mention the correct option after finding the solution, since it is a multiple choice question.

Complete step-by-step answer:

We have been asked to find out the value of $\dfrac{{\tan {{70}^0} - \tan {{20}^0}}}{{\tan {{50}^0}}}$

So, now we will make use of the formula

$\tan (x - y) = \dfrac{{\tan x - \tan y}}{{1 + \tan x\tan y}}$

So, from this we get tanx-tany=tan(x-y)(1+tanxtany)

So, let us express the numerator in this from, so we get

$\dfrac{{\tan ({{70}^0} - {{20}^0})(1 + \tan {{70}^0}.\tan {{20}^0})}}{{\tan {{50}^0}}}$

Now, in the denominator,

$\tan {50^ \circ } = \tan ({70^ \circ } - {20^ \circ })$

So, we can write the expression as

$\dfrac{{\tan ({{70}^ \circ } - {{20}^ \circ })(1 + \tan {{70}^ \circ }.\tan {{20}^ \circ })}}{{\tan ({{70}^ \circ } - {{20}^ \circ })}}$

So, from this,

$\tan ({70^ \circ } - {20^ \circ })$ in the numerator and denominator would get cancelled out

So, we get the equation as:

$(1 + \tan {70^ \circ }\tan {20^ \circ })$

Now, this can be further written as \[(1 + \tan ({90^ \circ } - {20^ \circ })\tan {20^ \circ })\]

We , also know the result which says $\tan ({90^ \circ } - \theta ) = \cot \theta $

So, from this we get $1 + \cot {20^ \circ }\tan {20^ \circ }$

Since, cot and tan are reciprocal of each other,

We can write $1 + \dfrac{1}{{\tan {{20}^ \circ }}} \times \tan {20^ \circ }$

=1+1=2

So, from this, we can write $\dfrac{{\tan {{70}^0} - \tan {{20}^0}}}{{\tan {{50}^0}}} = 2$

So, option A is the correct answer for this question

Note: Make use of the appropriate trigonometric formula which is needed and then from that obtain the needed result , also make sure to mention the correct option after finding the solution, since it is a multiple choice question.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE