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If tan θ + cot θ = 2, then the value of tan2θ + cot2θ is (SSC CGL 1st Sit. 2013)
- a)2
- b)1
- c)√2
- d)0
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If tan θ + cot θ = 2, then the value of tan2θ + cot2...
tan θ + cot θ = 2
On squaring both sides,
(tan θ + cot θ)2 = 4
⇒ tan2θ + cot2θ + 2tanθ cotθ = 4
⇒ tan2θ + cot2θ = 4 – 2 = 2 [tan θ. cot θ = 1]
On squaring both sides,
(tan θ + cot θ)2 = 4
⇒ tan2θ + cot2θ + 2tanθ cotθ = 4
⇒ tan2θ + cot2θ = 4 – 2 = 2 [tan θ. cot θ = 1]
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Community Answer
If tan θ + cot θ = 2, then the value of tan2θ + cot2...
Given
tan θ + cot θ = 2
To Find
tan2θ + cot2θ
Solution
Step 1: Squaring the given equation
(tan θ + cot θ)2 = 22
tan2θ + cot2θ + 2tan θ cot θ = 4
Step 2: Using trigonometric identities
tan θ cot θ = 1
Therefore, 2tan θ cot θ = 2
Step 3: Substituting the value in the equation
tan2θ + cot2θ + 2 = 4
tan2θ + cot2θ = 4 - 2
tan2θ + cot2θ = 2
Therefore, the value of tan2θ + cot2θ is 2. So, the correct answer is option 'A'.
tan θ + cot θ = 2
To Find
tan2θ + cot2θ
Solution
Step 1: Squaring the given equation
(tan θ + cot θ)2 = 22
tan2θ + cot2θ + 2tan θ cot θ = 4
Step 2: Using trigonometric identities
tan θ cot θ = 1
Therefore, 2tan θ cot θ = 2
Step 3: Substituting the value in the equation
tan2θ + cot2θ + 2 = 4
tan2θ + cot2θ = 4 - 2
tan2θ + cot2θ = 2
Therefore, the value of tan2θ + cot2θ is 2. So, the correct answer is option 'A'.
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If tan θ + cot θ = 2, then the value of tan2θ + cot2θ is (SSC CGL 1st Sit. 2013)a)2b)1c)√2d)0Correct answer is option 'A'. Can you explain this answer?
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