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  • The value of sin (45° + θ) – cos (45°–θ) is A. 2 cos θ B. 2sin θ C. 1 D. 0

The value of \sin (45 ^{\circ} + \theta ) - \cos (45 ^{\circ} - \theta )  is

A. 2 \cos \theta

B. 2\sin \theta

C. 1

D. 0

Answers (1)

The answer is the option (d). 

\\ \sin \left( 45+ \theta \right) - \cos \left( 45 - \theta \right) \\\\ \sin \left( 45+ \theta \right) =\sin 45\cos \theta +\cos 45\sin \theta =\frac{1}{\sqrt {2}}\cos \theta +\frac{1}{\sqrt {2}}\sin \theta \\\\ \cos \left( 45 - \theta \right) =\cos 45\cos \theta +\sin 45\sin \theta =\frac{1}{\sqrt {2}}\cos \theta +\frac{1}{\sqrt {2}}\sin \theta \\\\ \sin \left( 45+ \theta \right) - \cos \left( 45 - \theta \right) =\frac{1}{\sqrt {2}}\cos \theta +\frac{1}{\sqrt {2}}\sin \theta - \frac{1}{\sqrt {2}}\cos \theta - \frac{1}{\sqrt {2}}\sin \theta =0 \\\\

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infoexpert21

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