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.

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