Question
Evaluate the following$: \sin(35^\circ + \theta ) - \cos(55^\circ - \theta ) - \tan(42^\circ + \theta ) + \cot(48^\circ - \theta )$
✓
Answer
$\sin(35^\circ + \theta ) - \cos(55^\circ - \theta ) - \tan(42^\circ + \theta ) + \cot(48^\circ - \theta )$
$= \sin[90^\circ - (55^\circ - \theta )] - \cos(55^\circ - \theta ) - \tan[90^\circ - (48^\circ - \theta )] + \cot(48^\circ - \theta )$
$= \cos(55^\circ - \theta ) - \cos(55^\circ - \theta ) - \cot(48^\circ - \theta ) + \cot(48^\circ - \theta )$
$= 0.$
$= \sin[90^\circ - (55^\circ - \theta )] - \cos(55^\circ - \theta ) - \tan[90^\circ - (48^\circ - \theta )] + \cot(48^\circ - \theta )$
$= \cos(55^\circ - \theta ) - \cos(55^\circ - \theta ) - \cot(48^\circ - \theta ) + \cot(48^\circ - \theta )$
$= 0.$
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