Question
Download Solution PDFcos(30° + θ) - sin(60° - θ) = _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
cos (A + B) = cos A cos B - sin A sin B
sin (A - B) = sin A cos B - cos A sin B
Calculations:
cos(30° + θ) - sin(60° - θ)
cos30° × cosθ - sin θ sin 30° - (sin60° cos θ - cos60° sinθ)
cos30° × cosθ - sin θ sin 30° - sin60° cos θ + cos60° sinθ
Since,
cos 30° = √3/2, sin 30° = 1/2 and
cos 60° = 1/2, sin 60° = √3/2
⇒ (√3/2) cosθ - (1/2)sinθ - (√3/2)cosθ + (1/2)sinθ
⇒ (√3/2) cosθ - (1/2)sinθ - (√3/2)cosθ + (1/2)sinθ
= 0
Hence, The Required value is 0.
Last updated on Jul 22, 2025
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