Question

if (tan theta+1/tan theta)^2=2 then the value of tan^3 theta+1/tan^3 theta will be

Answer 1

Answer :

Given,

(tanθ + 1/tanθ)² = 2

⇒ tanθ + 1/tanθ = √2 ...(i)

Also,

(tanθ + 1/tanθ)² = 2

⇒ tan²θ + 1/tan²θ + 2 (tanθ) (1/tanθ) = 2

⇒ tan²θ + 1/tan²θ + 2 = 2

⇒ tan²θ + 1/tan²θ = 0 ...(ii)

Now, tan³θ + 1/tan³θ

= (tanθ + 1/tanθ) {tan²θ + 1/tan²θ - (tanθ) (1/tanθ)}

= √2 (0 - 1), by (i) and (ii)

= - √2

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