1st thing to be notice is that between sin A and CosA there is +ve sign and same case with TanA and cot A
or,
sin A+CosA=√2,--(1).
to find -->tan A+cot A=?
dividing (1).by cos A we get
tan A+1=√2,
tan A=√2-1 --(2).
now dividing (1) by sin A we get,
1+cot A=√2,
CotA=√2-1--(2).
from (1) and (2)
tan A=cot A=√2-1={A=45degree },
or, TanA+CotA=tan45+cot45=1+1=2

Given:
sinA cosA = √2

To find:
The value of tanA cotA

Solution:

Step 1: Rearrange the given equation
sinA cosA = √2
Divide both sides by cosA
sinA = √2 / cosA

Step 2: Apply the trigonometric identity
sinA = √(1 - cos^2A)
(sinA)^2 = (1 - cos^2A)
1 - (cosA)^2 = (sinA)^2

Step 3: Substitute the value of sinA from step 1
1 - (cosA)^2 = (√2 / cosA)^2
1 - (cosA)^2 = 2 / (cosA)^2
Multiply both sides by (cosA)^2
(cosA)^2 - (cosA)^4 = 2

Step 4: Substitute x = (cosA)^2
x - x^2 = 2

Step 5: Rearrange the equation
x^2 - x + 2 = 0

Step 6: Solve the quadratic equation
Using the quadratic formula, we have:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -1, and c = 2

x = (1 ± √((-1)^2 - 4(1)(2))) / 2(1)
x = (1 ± √(1 - 8)) / 2
x = (1 ± √(-7)) / 2

Since the square root of a negative number is not defined in real numbers, there are no real solutions for x. Therefore, there is no real value for cosA that satisfies the given equation sinA cosA = √2.

Hence, it is not possible to calculate the value of tanA cotA based on the given information.