If sec α × sin 59 ° = 1 then what is the value of α?1. 31°2. 21°

1.	If sec α × sin 59 ° = 1 then what is the value of α?1. 31°2. 21°3. 59°4. 39°
Answer» Correct Answer - Option 1 : 31° Given: It is given that sec α × sin 59 ° = 1 Formula Used: Basic concept of trigonometric ratio and identities We know that 1/cosec θ = sin θ Cosec (90 - θ) = sec θ Calculation: We know that the reciprocal of sin θ is cosec θ ∴ Sec α × sin 59 ° = 1 can be written as sec α × 1/cosec 59 ° = 1 ⇒ Sec α = cosec 59 ° ⇒ Sec α = cosec (90 - 31) ° ∵ Cosec (90 - θ) = sec θ ∴ Sec α = sec 31° ⇒ α = 31° Hence, option (1) is correct

If sec α × sin 59 ° = 1 then what is the value of α?1. 31°2. 21°3. 59°4. 39°

Answer» Correct Answer - Option 1 : 31°

Given:

It is given that sec α × sin 59 ° = 1

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

1/cosec θ = sin θ

Cosec (90 - θ) = sec θ

Calculation:

We know that the reciprocal of sin θ is cosec θ

∴ Sec α × sin 59 ° = 1 can be written as sec α × 1/cosec 59 ° = 1

⇒ Sec α = cosec 59 °

⇒ Sec α = cosec (90 - 31) °

∵ Cosec (90 - θ) = sec θ

∴ Sec α = sec 31°

⇒ α = 31°

Hence, option (1) is correct