Q. 84.1( 207 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 : Cos^{2}A – Sin^{2}A 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}

= (4*k*)^{2} + (3*k*)^{2}

= 16*k*^{2} + 9*k*^{2}

= 25*k*^{2}

AC = 5*k*

Cos A =

=

=

And also we know that,

Sin A =

=

=

And ,Tan A =

=

=

Now putting the values so obtained we get,

= 7/25

Cos^{2}A – Sin^{2}A =

=

=

Therefore,

Cos^{2}A – Sin^{2}A

Hence, the expression is correct.

Rate this question :

Draw the graph of 2x – 3y = 4. From the graph, find whether x = -1, y = -2 is a solution or not. (Final)

NCERT - MathematicsIf , find the value of

RD Sharma - MathematicsIf , find the value of

RD Sharma - MathematicsIf , find the value of

If , find all other trigonometric ratios of angle

RD Sharma - MathematicsIf , find the value of

RD Sharma - MathematicsIf , find the value of

RD Sharma - MathematicsIf , show that

RD Sharma - MathematicsIf , find

RD Sharma - MathematicsIf , find the value of

RD Sharma - Mathematics