If sec (A + B) = √2 and sin (A - B) = 1 then find the value of 2A +

1.	If sec (A + B) = √2 and sin (A - B) = 1 then find the value of 2A + B?1. 112.5°2. 87.5°3. 92.5°4. 109.5°
Answer» Correct Answer - Option 1 : 112.5° Given: It is given that sec (A + B) = √2 and sin (A - B) = 1 Formula Used: Basic concept of trigonometric ratio and identities We know that Sec 45° = √2 and sin 90° = 1 Calculation: The equation sec (A + B) = √2 can be written as ∵ Sec 45° = √2 ∴ Sec (A + B) = Sec 45° ⇒ A + B = 45° ---(1) And sin (A - B) = 1 so it can be written as ∵ Sin 90° = 1 ∴ sin (A - B) = Sin 90° ⇒ A - B = 90° ---(2) By equation (1) and (2) we get ∴ A = 67.5° and B = -22.5 ° Now, we have to find the value of 2A + B ∴ 2 × 67.5 + (-22.5) = 112.5° Hence, option (1) is correct

If sec (A + B) = √2 and sin (A - B) = 1 then find the value of 2A + B?1. 112.5°2. 87.5°3. 92.5°4. 109.5°

Answer» Correct Answer - Option 1 : 112.5°

Given:

It is given that sec (A + B) = √2 and sin (A - B) = 1

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Sec 45° = √2 and sin 90° = 1

Calculation:

The equation sec (A + B) = √2 can be written as

∵ Sec 45° = √2

∴ Sec (A + B) = Sec 45°

⇒ A + B = 45° ---(1)

And sin (A - B) = 1 so it can be written as

∵ Sin 90° = 1

∴ sin (A - B) = Sin 90°

⇒ A - B = 90° ---(2)

By equation (1) and (2) we get

∴ A = 67.5° and B = -22.5 °

Now, we have to find the value of 2A + B

∴ 2 × 67.5 + (-22.5) = 112.5°

Hence, option (1) is correct