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  1. If tan A + cot A = 2, then the value of tan10A + cot10A is
    1. 4
    2. 5
    3. 2
      10
    4. 1
Correct Option: B

tanA + cotA = 2

⇒ tanA +
1
= 2
tan A

⇒
tan²A + 1
= 2
tan A

⇒ tan²A + 1 = 2 tanA
⇒ tan²A – 2 tanA + 1 = 0
⇒ (tan A – 1)² = 0
⇒ tan A – 1= 0
⇒ tan A = 1
⇒ cot A = 1
∴ tan10 A + cot10 A = 1 + 1 = 2


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