tanA+4cotA=4 find the value of tanA*tanA+cotA*cotA
tanA + 4/tanA = 4
(tan^2A+4)/tanA = 4
tan^2A - 4tanA + 4 = 0
(tanA-2)^2 = 0
tanA = 2
...
To find the value of tanA*tanA + cotA*cotA, we need to manipulate the given equation and apply trigonometric identities.
Starting with the given equation: tanA + 4cotA = 4
First, let's convert cotA to its equivalent form in terms of tanA:
cotA = 1/tanA
Substituting this into the equation, we get:
tanA + 4 * (1/tanA) = 4
Now, let's simplify this equation:
Multiply through by tanA to eliminate the fraction:
tanA * tanA + 4 = 4 * tanA
Rearranging:
tanA * tanA - 4 * tanA + 4 = 0
Now, we have a quadratic equation in terms of tanA. To solve for tanA, we can use the quadratic formula:
tanA = (-b ± √(b^2 -4ac)) / 2a
In this case, a = 1, b = -4, and c = 4. Substituting these values, we have:
tanA = (-(-4) ± √((-4)^2 - 4*1*4)) / (2 * 1)
= (4 ± √(16 - 16)) / 2
= (4 ± √0) / 2
Since the discriminant (b^2 - 4ac) is zero, we get only one real solution:
tanA = 4/2
= 2
Now, to find tanA * tanA + cotA * cotA, we substitute the value of tanA into the equation:
tanA * tanA + cotA * cotA = 2 * 2 + (1/2) * (1/2)
= 4 + (1/4)
= 17/4