If tan 4θ = cot (θ – 2) then find the value of 7θ?
1. 102.2°
2. 125.5°
3. 118.3°
4. 128.8°
1. 102.2°
2. 125.5°
3. 118.3°
4. 128.8°
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Correct Answer – Option 4 : 128.8°
Given:
The given condition is tan 4θ = cot (θ – 2)
Formula Used:
Basic concept of trigonometric ratio and identities
We know that
tan θ = cot (90 – θ)
Calculation:
∵ Cot θ = tan (90 – θ)
∴ cot (90 – 4θ) = cot (θ – 2)
⇒ (90 – 4θ) = (θ – 2)
⇒ θ = 18.4°
Now, we have to find the value of 7θ = 7 × 18.4° = 128.8°
Hence, option (4) is correct