Q2 of 54 Page 312

Without using trigonometric tables, prove that:
cos257° - sin233° = 0

Consider cos2 57° - sin2 33° = cos2 57° - sin2 (90 - 57)°

= cos2 57° - cos2 57°


= 0


Hence, proved.


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tan266° - cot224° = 0

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(sin 65° + cos 25°)(sin 65° - cos 25°) = 0

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sin 53° cos 37° + cos 53° sin 37° = 1