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If tan θ + cot θ = 2 then tan10θ - cot10θ, 0 < θ < 90, will be equal to 

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Correct Answer - Option 1 : 0

Formula used:

\(\tan\ θ =\frac{1}{cot\ θ}\)

(a - b)2 = a2 - 2ab + b2

Calculation:

Given that,

tan θ + cot θ = 2

⇒ tan θ + 1/tan θ = 2

⇒ tan2 θ - 2 tan θ  + 1 = 0

⇒ (tan θ - 1)2 = 0

⇒ tan θ  = ± 1  

⇒ tan θ = 1 = cot θ      (∵  0 < θ < 90)

Hence, required value of 

tan10θ - cot10θ

=  1 - 1

= 0

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