Answer:
Proof is given below.
[tex]tan^2 45\°+cot^2 45\° \ne 1[/tex]
Step-by-step explanation:
To prove: [tex]tan^2 A+cot^2 A = 1[/tex] 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;
[tex]tan^2 45\°+cot^2 45\°=(1)^2 +(1)^2=1+1=2[/tex]
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, [tex]tan^2 45\°+cot^2 45\° \ne 1[/tex]
So, this violates the given equation and hence the given equation is not always true. So, it's not a trigonometric identity.
