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If tan A + cot A = 2, then the value of tan10A + cot10A is?
- A210
- B1
- C2
- D4
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CCommunity
Given,
tan A + cot A = 2
As, cotA = 1/tanA
$(\Rightarrow \tan A + \frac{1}{{tanA}} = 2)$
⇒ tan2 A + 1 = 2tanA
⇒ tan2 A + 1 - 2tanA = 0
⇒ (tanA – 1)2 = 0 {using, (a – b)2 = a2 + b2 -2ab}
⇒ tanA = 1
∴ cotA = 1/1 = 1
We need to find the value of
tan10A + cot10A= (1)10 + (1)10
= 1 + 1
= 2
tan A + cot A = 2
As, cotA = 1/tanA
$(\Rightarrow \tan A + \frac{1}{{tanA}} = 2)$
⇒ tan2 A + 1 = 2tanA
⇒ tan2 A + 1 - 2tanA = 0
⇒ (tanA – 1)2 = 0 {using, (a – b)2 = a2 + b2 -2ab}
⇒ tanA = 1
∴ cotA = 1/1 = 1
We need to find the value of
tan10A + cot10A= (1)10 + (1)10
= 1 + 1
= 2