Q. 1 If $sin θ + cos θ =\sqrt2$ , then find the value of $tan θ + cot θ$ .

%. If sinθ + cosθ = √2, then find the value of tanθ + cotθ.

Consider the given equation,

sin θ + cos θ = \sqrt 2

…(1)

Taking square both sides,

(sin θ + cos θ)² = (\sqrt 2)²

sin² θ + cos² θ + 2 sin θ cos θ = 2

1 + 2 sin θ cos θ = 2

2 sin θ cos θ = 1

sin θ cos θ = 1/2

……(2)

Now, divided by

cos θ

in equation 1^st , we get

tan θ + 1 =\sqrt2/ cos θ

….(3)

Again divided by

sin θ

in equation 1^st, we get

1 + cot θ =\sqrt2/ sin θ

….(4)

Add equation 1^st and 2^nd , we get

tanθ+cotθ+1+1=√2/cosθ+√2/sinθ

tan θ + cot θ + 2 = (sin θ + cos θ)/sinθcosθ

tanθ+cotθ+2=√2(√2)/1/2 ……(5)

tanθ+cotθ+2=(2)/1/2

tanθ+cotθ+2=(2)×2/1

tanθ+cotθ =4 –2

Now, from equation 1^st ,2^nd and 5^th ,we get

tanθ+cotθ=2

Hence, this is the answer.

If sinθ + cosθ = √2, then find the value of tanθ + cotθ.