Question

If tan^2theta+cot^2theta=17/4 Then tan theta+cot that's =

Answer 1

Answer:

let tana = x

cota = 1/x

now,

x²+1/x² = 17/4

adding 2 both sides we get,

x²+1/x² +2 = 17/4 + 2

(x+1/x)² = 25/4

x+1/x = 5/2

so,

tana+1/cota = 5/2 (Ans)

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Answer 2

The value of tanθ + cotθ would be equal to 5/2.

Given:

tan²θ + cot²θ = 17/4

To Find:

The value of tanθ + cotθ

Solution:

Let tan θ = x therefore cot θ = 1/x

∵ tan²θ + cot²θ = 17/4

         $x^{2} +(\frac{1}{x} )^{2} =\frac{17}{4}$

→ Now adding 2 on both sides to make a whole square term on the L.H.S.

        $x^{2} +(\frac{1}{x} )^{2}+2 =\frac{17}{4}+2\\\\(x +\frac{1}{x} )^2=\frac{25}{4}\\\\x+\frac{1}{x} =\frac{5}{2}$

  ∴ tanθ + cotθ = 5/2.

Hence the value of tanθ + cotθ comes out to be equal to 5/2.

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