Question

If sectheta - tantheta = 5/2, find sectheta, tantheta, cottheta, costheta.​

Answer 1

Solution

Given :-

• Sec θ - tan θ = 5/2 -------(1)

Find :-

• Value of tan θ , Sec θ , cot θ & cos θ

Explanation

Using Formula

★ Sec²θ - tan² θ = 1

★ tan θ = 1/cot θ

★ Sec θ = 1/cos θ

Now,

➥ Sec²θ - tan² θ = 1

[ (a²-b²) = (a-b)(a+b) ]

➥( Secθ - tanθ)(Secθ + tanθ) = 1

Keep value by equ(1)

➥ (Secθ + tanθ) * 5/2 = 1

➥ (Secθ + tanθ) = 1 - 5/2

➥ (Secθ + tanθ) = (2-5)/2

➥ (Secθ + tanθ) = -3/2 -----------(2)

Add equ(1) & equ(2)

➥ (Secθ + Secθ) = 5/2 + (-3/2)

➥ 2 sec θ = 5/2 - 3/2

➥ 2 sec θ = (5-3)/2

➥ 2 sec θ = 2/2

➥ 2 sec θ = 1

➥ sec θ = 1/2

Keep value of sec θ in equ(2)

➥ 1/2 + tanθ = -3/2

➥ tanθ = -3/2 - 1/2

➥ tanθ = (-3-1)/2

➥ tanθ = -4/2

➥ tanθ = -2

Now, Calculate Value of cot θ & cos θ

➥ Cot θ = 1/tanθ

Keep value of tanθ,

➥ Cot θ = 1/(-2)

Or,

➥ Cot θ = -1/2

Again,

➥ Cos θ = 1/Secθ

Keep Value of Secθ,

➥ Cos θ = 1/(1/2)

➥ Cos θ = 2

Hence

• Value of Sec θ = 1/2
• Value of tan θ = -2
• Value of cos θ = 2
• Value of cot θ = -1/2

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Answer 2

Answer:

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