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