Nilai cos(-15°)-sin 165° adalah....

<p>Jawaban yang benar adalah (1/2)√2</p><p>&nbsp;</p><p>Konsep :</p><p>cos (-a) = cos a</p><p>sin (180°-a) = sin a</p><p>sin (a - b) = sin a cos b – cos a sin b</p><p>cos (a - b) = cos a cos b + sin a sin b</p><p>&nbsp;</p><p>Pembahasan :</p><p>cos (-15°) = cos 15°</p><p>= cos (45°-30°)&nbsp;</p><p>= cos 45° · cos 30° + sin 45° · sin 30°</p><p>= (1/2)√2 · (1/2)√3 + (1/2)√2 · (1/2)&nbsp;</p><p>= (1/2) · (1/2) · √(2·3) + (1/2) · (1/2) √2</p><p>= (1/4)√6 + (1/4)√2</p><p>&nbsp;</p><p>sin 165° = sin (180°-15°)&nbsp;</p><p>= sin 15°</p><p>= sin (45°-30°)&nbsp;</p><p>= sin 45° · cos 30° - cos 45° · sin 30°</p><p>= (1/2)√2 · (1/2)√3 – (1/2)√2 · (1/2)&nbsp;</p><p>= (1/2) · (1/2) · √(2·3) – (1/2) · (1/2) √2</p><p>= (1/4)√6 – (1/4)√2</p><p>&nbsp;</p><p>cos(-15°)-sin 165° = (1/4)√6 + (1/4)√2 – ((1/4)√6 – (1/4)√2)&nbsp;</p><p>= (1/4)√6 + (1/4)√2 – (1/4)√6 + (1/4)√2</p><p>= &nbsp;(1/4)√6 – (1/4)√6 + (1/4)√2 + (1/4)√2</p><p>= (2/4)√2</p><p>= (1/2)√2</p><p>&nbsp;</p><p>Jadi diperoleh nilai dari cos(-15°)-sin 165° = (1/2)√2</p>