Question

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

Answer 1

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

Answer 2

Answer:

$35/12$

Step-by-step explanation:

It is the correct answer.

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