If sin θ + cos θ = √5 sin(90 – θ), find the value of cot θ.
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Correct answer: B
Explanation
The correct answer is Option 2. i.e. √(5 + 1) /4
Given:
sin θ + cos θ = √5 sin(90 – θ)
Concept Used:
sin(90 - θ) = cosθ .....(i)
sinθ/cosθ = tanθ .....(ii)
Explanation:
Using equation (i) in the given question, we get
sinθ + cosθ = √5 cosθ .....(iii)
Dividing equation (iii) by cosθ, we get
sinθ/cosθ + 1 = √5
⇒ tanθ = √5 - 1
Since, 1/tanθ = cotθ
⇒ cotθ = 1/(√5 - 1)
On rationalising the above value,
⇒ cotθ = (√5 + 1)/4
Hence the value of cotθ is (√5 + 1)/4.