If sin q + cos q = then what is the value of tan q + cotq ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 8(√3 - 2).
Calculations:
⇒ tan θ + cot θ = 1/(sin θ.cosθ) ---- (1)
⇒ (sin θ + cos θ) = ((√3 - 1)/2√2)
Squaring on both sides we get
⇒ 1 + 2sinθ.cosθ = (4 - 2√3)/8
⇒ sinθ.cosθ = - (4 + 2√3)/16
Now using the value of sinθ.cosθ in equation (1)
⇒ (16/-(4 + 2√3))
Rationalising the denominator, we get
⇒ 16(2√3 - 4)/4 = 8(√3 - 2)