If Sec Ɵ = 5/4, show that (tan theta -cot theta) / (sin theta – cos theta) = 7/12

2 thoughts on “If Sec Ɵ = 5/4, show that (tan theta -cot theta) / (sin theta – cos theta) = 7/12”

1. Answer:

   [tex]35/12[/tex]

   Step-by-step explanation:

   It is the correct answer.

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2. Given

   ⇒Secθ = 5/4

   show that

   ⇒(Tanθ – Cotθ)/(Sinθ – Cosθ) = 7/12

   Now we know that

   ⇒Secθ = 5/4 = Hypotenuse(h)/Base(b)

   We get

   ⇒Hypotenuse(h) = 5 , Base(b) = 4 and Perpendicular(p) = x

   using Pythagoras theorem

   ⇒h² = b² + p²

   ⇒(5)² = (4)² + p²

   ⇒25 = 16 + p²

   ⇒p² = 25 – 16

   ⇒p² = 9

   ⇒p = 3

   We get

   ⇒Hypotenuse(h) = 5 , Base(b) = 4 and Perpendicular(p) = 3

   We know that

   ⇒Tanθ = p/b = 3/4

   ⇒Cotθ = b/p = 4/3

   ⇒Sinθ = p/h = 3/5

   ⇒Cosθ = b/h = 4/5

   Put the value

   ⇒(Tanθ – Cotθ)/(Sinθ – Cosθ)

   ⇒(3/4 – 4/3)/(3/5 – 4/5)

   ⇒{(9 – 16)/12}/(-1/5)

   ⇒(-7/12)/(-1/5)

   ⇒7/12×5

   ⇒35/12

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