Math, asked by Anonymous, 11 months ago

If 3 cot A = 4, check whether (1-tan²A)/(1+tan²A) = cos² A – sin² A or not.​

Answers

Answered by Anonymous
13

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Solution:

Let us consider a triangle ABC, right-angled at B.

As per the given question,

cot A = 4/3 = AB/BC

So, AB = 4k and BC = 3k, where k is any positive integer.

Using Pythagoras theorem,

AC² = AB² + BC²

Putting the values of AB and BC, we get;

AC² = (4k)² + (3k)²

AC² = 16k² + 9k²

AC = √25k² = 5k

Now we have all the sides.

As we know,

tan A = 1/cot A

tan A = 3/4

sin A = BC/AC = 3/5

cos A = AB/AC = 4/5

To check: (1-tan²A)/(1+tan²A) = cos² A – sin² A or not

Let us take L.H.S. first;

(1-tan²A)/(1+tan²A) = 1-(3/4)²/1+(3/4)²

= [1-9/16]/[1+9/16] = 7/25

R.H.S. = cos² A – sin² A = (4/5)²-(3/5)²

= (16/25) – (9/25) = 7/25

Since,

L.H.S. = R.H.S.

.Hence, proved.

Answered by Anonymous
2

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