Question

If Sec thita+Tan this =P then Sec thita -Tan thita =​

Answer 1

Q: If sec θ + tan θ = P then sec θ - tan θ =

Solution:

⟶ sec θ + tan θ = P

• Multiplying (sec θ - tan θ) both sides.

⟶ (sec θ + tan θ) (sec θ - tan θ) = P (sec θ - tan θ)

⟶ sec² θ - tan² θ = P (sec θ - tan θ)

⟶ 1 = P (sec θ - tan θ)

⟶ (sec θ - tan θ) = 1/P

Answer: sec θ - tan θ = 1/P

Algebraic Identities used:

• (a + b) (a - b) = a² - b²

Trigonometric Indentities used:

• sec² θ - tan² θ = 1

More Trigonometric Indentities:

• sin²θ + cos²θ = 1
• 1 - sin²θ = cos²θ
• 1 - cos²θ = sin²θ
• cosec²θ - cot²θ = 1
• cosec²θ - 1 = cot²θ
• 1 + cot²θ = cosec²θ
• sec²θ - tan²θ = 1
• sec²θ - 1 = tan²θ
• 1 + tan²θ = sec²θ
• cot²θ • tan²θ = 1
• sec²θ • cos²θ = 1
• sin²θ • cosec²θ = 1

Answer 2

Given

• sec θ + tan θ = P

To find

• sec θ - tan θ

Solution

We know, sec² θ + tan² θ = 1

Then, now we get :-

• ( sec θ + tan θ ) ( sec θ - tan θ ) = 1
• p × ( sec θ - tan  θ ) = 1
• ( sec θ - tan θ ) = 1 / p

∴ sec θ - tan θ = 1/p