Question

Prove that tan^2A + cot^2A = 1 is not a trigonometric identity by producing a counterexample​

Answer 1

Answer:

Proof is given below.

$tan^2 45\°+cot^2 45\° \ne 1$

Step-by-step explanation:

To prove: $tan^2 A+cot^2 A = 1$ is not a trigonometric identity.

A trigonometric identity is an equation whose left hand side is always to the right hand side for any value of the given angle.

A counterexample is a method used to counter the given statement by taking a random value for the given quantity and disproving the left and right side of the equation.

So, let us take A = 45°

Then, left hand side of the equation becomes;

$tan^2 45\°+cot^2 45\°=(1)^2 +(1)^2=1+1=2$

Therefore, the value of left hand side of the equation on plugging in 45° for A gives the result as 2.

But the right hand side of the equation is equal to 1.

Therefore, $tan^2 45\°+cot^2 45\° \ne 1$

So, this violates the given equation and hence the given equation is not always true. So, it's not a trigonometric identity.