Q. 84.1( 248 Votes )

If 3 cot A = 4, check whether      or not

Answer :

It is given that 3 cot A = 4

                     


Consider a right triangle ABC, right-angled at point B



To Find : Cos2A – Sin2A  or not



Cot A =


=


This fraction shows that if the length of base will be 4 then the altitude will be 3. And base and altitude will both increase with this propotion only. Let AB be 4k then BC will be 3k


In ΔABC,
Pythagoras theorem :  It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
By pythagoras theorem


(AC)2 = (AB)2 + (BC)2


= (4k)2 + (3k)2


= 16k2 + 9k2


= 25k2


AC = 5k

Now,

Cos A =


=


=


And also we know that,

Sin A =  


=


=

And ,

Tan A =


=


=

Now putting the values so obtained we get,

     
         = 7/25

Cos2A – Sin2A = 


=


=


Therefore,


 Cos2A – Sin2A
Hence, the expression is correct.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric IdentitiesTrigonometric IdentitiesTrigonometric Identities44 mins
Champ Quiz | Trigger on TrigonometryChamp Quiz | Trigger on TrigonometryChamp Quiz | Trigger on Trigonometry47 mins
Basics of TrigonometryBasics of TrigonometryBasics of TrigonometryFREE Class
NCERT |  Imp. Qs. Discussion - TrigonometryNCERT |  Imp. Qs. Discussion - TrigonometryNCERT | Imp. Qs. Discussion - Trigonometry44 mins
NCERT | Imp. Qs. on TrigonometryNCERT | Imp. Qs. on TrigonometryNCERT | Imp. Qs. on Trigonometry42 mins
Quiz | Trail of Mixed Questions on TrigonometryQuiz | Trail of Mixed Questions on TrigonometryQuiz | Trail of Mixed Questions on Trigonometry59 mins
NCERT | Trigonometric IdentitiesNCERT | Trigonometric IdentitiesNCERT | Trigonometric Identities52 mins
NCERT | Discussion on Imp. Qs. of TrignometryNCERT | Discussion on Imp. Qs. of TrignometryNCERT | Discussion on Imp. Qs. of Trignometry45 mins
Champ Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important Questions33 mins
Solving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric Identities56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses