Question

If sin A+ cos A = root 2 cos A then find value of cot A

Answer 1

(sin A + cos A )/cos A = ✓2
=> sin A/cos A + cos A / cos A = ✓2
=> tan A + 1 = ✓2
=> tan A= ✓2-1
=> cot A = 1/✓2-1
=> cot A = 1/✓2-1 * ✓2+1/✓2+1
=> cot A = ✓2+1/(✓2)²-1²
=> cot A = ✓2+1/2-1
=> cot A = ✓2+1

Answer 2

Answer:

cotA = (√2 + 1)

Step-by-step explanation:

Given: sinA + cosA = √2cosA

dividing by cosA in both side

sinA/cosA + cosA/cosA = √2cosA/cosA

tanA + 1 = √2

tanA = √2 - 1

cotA = 1/√2 - 1

cotA = 1/(√2 - 1) × (√2 + 1)/(√2 + 1)

cotA = (√2 + 1)/(2 - 1)

cotA = (√2 + 1)

thanks,

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