If secQ=5/4, Find the value of SinQ-2CosQ/TanQ-CotQ

1.	If secQ=5/4, Find the value of SinQ-2CosQ/TanQ-CotQ
Answer» Given :- secQ = (5/4) To Find :- (SinQ - 2CosQ) /(TanQ - CotQ) Formula used :- sin theta = Perpendicular/Hypotenuse cos theta = Base/Hypotenuse tan theta = Perpendicular/Base cosec theta = Hypotenuse/Perpendicular sec theta = Hypotenuse/Base cot theta = Base/Perpendicular Solution :- → secQ = (5/4) = Hypotenuse/Base So, → Hypotenuse = 5 → Base = 4 So, By PYTHAGORAS Theoram , → Perpendicular = √(5)² - (4)² → Perpendicular = √(25 - 16) → Perpendicular = √9 → Perpendicular = 3 . _______________ So, → SinQ = Perpendicular/Hypotenuse = 3/5 → cosQ = Base/Hypotenuse = 4/5 → TanQ = Perpendicular/Base = 3/4 → CotQ = Base/Perpendicular = 4/3 ________________ Putting All Values now, we get :- → (SinQ - 2CosQ) /(TanQ - CotQ) → [ (3/5) - 2(4/5) ] / [ (3/4) - (4/3) ] → [ (3- 8)/(5) ] [ ( 9 - 16) / (12) ] → (-5/5) / (-7/12) → (-1) (-12/7) → (12/7) (ANS).

Answer»

Given :-

→ secQ = (5/4) = Hypotenuse/Base

So,

→ Hypotenuse = 5

→ Base = 4

So, By PYTHAGORAS Theoram ,

→ Perpendicular = √(5)² - (4)²

→ Perpendicular = √(25 - 16)

→ Perpendicular = √9

→ Perpendicular = 3 .

→ SinQ = Perpendicular/Hypotenuse = 3/5

→ cosQ = Base/Hypotenuse = 4/5

→ TanQ = Perpendicular/Base = 3/4

→ CotQ = Base/Perpendicular = 4/3

Putting All Values now, we get :-

→ (SinQ - 2CosQ) /(TanQ - CotQ)

→ [ (3/5) - 2*(4/5) ] / [ (3/4) - (4/3) ]

→ [ (3- 8)/(5) ] [ ( 9 - 16) / (12) ]

→ (-5/5) / (-7/12)

→ (-1) * (-12/7)