Question

If Sec (A + B) = 2 and Sec (A - B) = 1, find A,B​

Answer 1

the answer to your question

Answer 2

Given:

• Sec (A + B) = 2
• Sec (A - B) = 1

To find:

• Values of A and B

Method:

We know that;

• Sec 60° = 2
• Sec 0° = 1

Sec (A + B) = 2

⇒ (A + B) = Sec⁻¹(2)

⇒ (A + B) = 60°  ------ [Equation 1]

Sec (A - B) = 1

⇒ (A - B) = Sec⁻¹(1)

⇒ (A - B) = 0° ------ [Equation 2]

Adding Equations 1 and 2,

        A + B = 60

  {+}  A - B =  0

        2A = 60°

⇒ A = 60 ÷ 2

⇒ A = 30°

Substitute Value of A in any one of the Equation.

Here we have substituted in Equation 1

A + B = 60°

⇒ 30° + B = 60°

⇒ B = 60° - 30°

⇒ B = 30°