Find the value of sin(60 + θ) - cos(30 - θ).

1.	Find the value of sin(60 + θ) - cos(30 - θ).
Answer» Correct Answer - Option 1 : 0 Formula Used: Sin(A +B) = SinACosB + CosASinB Cos(A – B) = CosACosB + SinASinB Calculation: ⇒ Sin(60 + θ) = Sin60×Cosθ + Cos60×Sinθ ⇒ Sin(60 + θ) = (√3/2)Cosθ + (1/2)Sinθ ----(1) ⇒ Cos(30 – θ) = Cos30×Cosθ + Sin30×Sinθ ⇒ Cos(30 – θ) = (√3/2)Cosθ + (1/2)Sinθ ----(2) ⇒ Now the value of Sin(60 + θ) – Cos(30 – θ) from (1) & (2) ⇒ (√3/2)Cosθ + (1/2)Sinθ – (√3/2)Cosθ - (1/2)Sinθ = 0 ∴ The answer is 0 Short Trick: Put θ = 0°, we get ⇒ Sin60 - Cos30 = 0 ∴ From both we get 0

Answer» Correct Answer - Option 1 : 0

Formula Used:

Sin(A +B) = SinACosB + CosASinB

Cos(A – B) = CosACosB + SinASinB

Calculation:

⇒ Sin(60 + θ) = Sin60×Cosθ + Cos60×Sinθ

⇒ Sin(60 + θ) = (√3/2)Cosθ + (1/2)Sinθ ----(1)

⇒ Cos(30 – θ) = Cos30×Cosθ + Sin30×Sinθ

⇒ Cos(30 – θ) = (√3/2)Cosθ + (1/2)Sinθ ----(2)

⇒ Now the value of Sin(60 + θ) – Cos(30 – θ) from (1) & (2)

⇒ (√3/2)Cosθ + (1/2)Sinθ – (√3/2)Cosθ - (1/2)Sinθ = 0

∴ The answer is 0

Short Trick:

Put θ = 0°, we get

⇒ Sin60 - Cos30 = 0

∴ From both we get 0

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