#### Find the value of θ if

(i) sin (θ + 36°) = cos θ, where θ and θ + 36° are acute angles.

(ii) sec 4θ = cosec (θ – 20°), where 4θ and θ – 20° are acute angles.

**Answer :**

**(i)** Given, θ and (θ + 36°) are acute angles

sin (θ + 36°) = cos θ = sin (90° – θ) **[As, sin (90° – θ) = cos θ]**

θ + 36° = 90° – θ

⇒ θ + θ = 90° – 36°

⇒ 2θ = 54°

⇒ θ = 54°/2

∴ θ = 27°

**(ii)** Given, θ and (θ – 20°) are acute angles

And,

sec 4θ = cosec (θ – 20°)

⇒ cosec (90° – 4θ) = cosec (θ – 20°) **[Since, cosec (90° – θ) = sec θ]**

On comparing, we get

90° – 4θ = θ – 20°

⇒ 90° + 20° = θ + 4θ

⇒ 5θ = 110°

⇒ θ = 110°/5

∴ θ = 22°

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