The value of sin (45° + θ) – cos(45°

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The value of sin (45° + θ) – cos(45° – θ) is

1. 2cosθ
2. 2sinθ
3. 1
4. 0

Correct Option: D

sin (45° + θ) – cos (45° – θ)
= sin 45° cosθ + cos 45° sinθ – (cos 45° cosθ + sin 45° sinθ)
∵ sin (A + B) = sinA cosB + cosA sinB
cos(A – B) = cosA cosB + sinA sinB

=	cosθ	+	sinθ	-	cosθ	-	sinθ	= 0
	√2		√2		√2		√2