Question

find the value of tan theta + cot theta

Answer 1

tan x + cot x=(sin²x+cos²x)/(sin x cos x)=1/(sin x cos x)

sin x+cos x=√2

Squaring it,

sin²x+cos²x+2sin x cos x=2

So, we can get sin x cos x from here and put it to get answer.

Answer 2

Answer:

The value of tanθ + cotθ is 2.

Step-by-step explanation:

Given,

sinθ + cosθ = $\sqrt{2}$      ---- (i)

we have to find,

tanθ + cotθ

⇒ sinθ/cosθ + cosθ/sinθ

⇒ sin²θ + cos²θ/(sinθcosθ)   ---- (ii)

squaring both sides of equation (i), we get

sin²θ + cos²θ + 2( sinθcosθ ) = 2

⇒ 1 + 2( sinθcosθ ) = 2   ( trigonometric identities)

⇒ 2( sinθcosθ ) = 1

⇒ sinθcosθ = 1/2      ---- (iii)

Using equations (ii) and (iii), we get

tanθ + cotθ = 1/(1/2)

tanθ + cotθ = 2

Hence, the value of tanθ + cotθ is 2.

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