Question:
sin (45° + θ) – cos (45° – θ) = ?
(a) 0
(b) 1
(c) 2
(d) –2
Solution:
$\sin \left(45^{\circ}+\theta\right)-\cos \left(45^{\circ}-\theta\right)$
$=\cos \left(90^{\circ}-\left(45^{\circ}+\theta\right)\right)-\cos \left(45^{\circ}-\theta\right) \quad\left(\because \sin \theta=\cos \left(90^{\circ}-\theta\right)\right)$
$=\cos \left(90^{\circ}-45^{\circ}-\theta\right)-\cos \left(45^{\circ}-\theta\right)$
$=\cos \left(45^{\circ}-\theta\right)-\cos \left(45^{\circ}-\theta\right)$
$=0$
Hence, the correct option is (a).
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