If sin (α - β) = 2√2/3 and cosec (α + β) = 2√2/3 then find the

1.	If sin (α - β) = 2√2/3 and cosec (α + β) = 2√2/3 then find the value of tan (α2 – β2)?1. tan 8/92. tan 93. tan 124. tan 15
Answer» Correct Answer - Option 1 : tan 8/9 Given: Sin (α - β) = 2√2/3 and cosec (α + β) = 2√2/3 Concept Used: Basic concept of trigonometric ratio and identities We know that (α² – β²) = (α - β) × (α + β) sin ^-1a × cosec ^-1a = 1 Calculation: It is given that sin (α - β) = 2√2/3 ∴ (α - β) = sin ^-12√2/3 ---(1) And cosec (α + β) = 2√2/3 ∴ (α + β) = cosec ^-12√2/3 ---(2) By multiplying equation (1) and (2) ∴ (α - β) × (α + β) = sin ^-12√2/3 × cosec ^-12√2/3 ⇒ (α² – β²) = 8/9 Now, tan (α² – β²) = tan 8/9 Hence, option (1) is correct

If sin (α - β) = 2√2/3 and cosec (α + β) = 2√2/3 then find the value of tan (α2 – β2)?1. tan 8/92. tan 93. tan 124. tan 15

Answer» Correct Answer - Option 1 : tan 8/9

Given:

Sin (α - β) = 2√2/3 and cosec (α + β) = 2√2/3

Concept Used:

Basic concept of trigonometric ratio and identities

We know that

(α² – β²) = (α - β) × (α + β)

sin ^-1a × cosec ^-1a = 1

Calculation:

It is given that sin (α - β) = 2√2/3

∴ (α - β) = sin ^-12√2/3 ---(1)

And cosec (α + β) = 2√2/3

∴ (α + β) = cosec ^-12√2/3 ---(2)

By multiplying equation (1) and (2)

∴ (α - β) × (α + β) = sin ^-12√2/3 × cosec ^-12√2/3

⇒ (α² – β²) = 8/9

Now, tan (α² – β²) = tan 8/9

Hence, option (1) is correct