If sinA+cosA=
3
4
​
, then find the value of tanA+cotA.

Given:
sinA+cosA=
3
4
​

Squaring both sides:

(sinA+cosA)
2
=(
3
4
​
)
2

sin
2
A+cos
2
A+2sinAcosA=
9
16
​

Since sin
2
A+cos
2
A=1:

1+2sinAcosA=
9
16
​

2sinAcosA=
9
16
​
−1=
9
7
​

sinAcosA=
18
7
​

Now, let's simplify the expression we need to find:

tanA+cotA=
cosA
sinA
​
+
sinA
cosA
​
=
sinAcosA
sin
2
A+cos
2
A
​
=
sinAcosA
1
​

Substitute the value of sinAcosA:

tanA+cotA=
18
7
​

1
​
=
7
18
​