What is the value of \frac{\sin 2^\circ \sin 4^\circ \sin6^\circ...\sin88^\circ}{\cos 88^\circ\cos 86^\circ\cos 84^\circ...\cos2^\circ}

Trigonometry Practice Test 1

Question : 32 of 40

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What is the value of

{\sin 2° \sin 4° \sin6°...\sin88°}/{\cos 88°\cos 86°\cos 84°...\cos2°}

Solution:

{\sin 2° \sin 4° \sin6°...\sin88°}/{\cos 88°\cos 86°\cos 84°...\cos2°}

={\sin 2° \sin 4° \sin6°...\sin88°}/{\cos (90°-2°)\cos (90°-4°) ...\cos (90°-88°)}

={\sin 2° \sin 4° \sin6°...\sin88°}/{\sin 2° \sin 4° \sin6°...\sin88°}=1

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