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If \( \Large A = 130 ^{\circ} and\ x=\sin A + \cos A \), then:

A) \( \Large x > 0 \)
B) \( \Large x < 0 \)
C) \( \Large x=0 \)
D) \( \Large x \le 0 \)

Correct Answer:

A) \( \Large x > 0 \)

Description for Correct answer:
Since, \( \Large A = 130 ^{\circ} \)

and \( \Large x = \sin A + \cos A \)

=> \( \Large x = \sin 130 ^{\circ} + \cos 130 ^{\circ} \)

= \( \Large \cos 40 ^{\circ} + \cos 130 ^{\circ} \)

= \( \Large 2 \cos \left(\frac{170 ^{\circ} }{2}\right) \cos \left(\frac{90 ^{\circ} }{2}\right) \)

= \( \Large 2 \cos 85 ^{\circ} \cos 45 ^{\circ} > 0 \)

=> \( \Large x > 0 \)

Part of solved Trigonometric ratio questions and answers : >> Elementary Mathematics >> Trigonometric ratio

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Similar Questions

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