If A lies in third quadrant, and 20tanA = 21, then the value of (5 SinA - 2 CosA)/(4 CosA - (5/7)SinA) is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e 1
⇒ tanA = perpendicular / base = 21 / 20
By using the pythogorus theorem,
⇒ Hypotenuse = √(441 + 400)
⇒ Hypotenuse = 29
⇒ SinA = perpendicular / hypotenuse = 21 / 29
As in 3rd quadrant sin will be negative, sinA = -21 / 29
⇒ CosA = base / hypotenuse = 20 / 29
As in 3rd quadrant sin will be negative, cosA = -20 / 29
⇒ (5 SinA - 2 CosA)/(4 CosA - (5/7)SinA)
⇒ {5(-21 / 29) - 2 × (-20 / 29)}/{4(-20 / 29) - (5/7) × (-21 / 29)}
⇒ {-65 / 29} / {-65 / 29}
⇒ 1