sin 270° x cos 135° +tan 135° ______________________________ sin 150° + sin 225°

<p>Jawaban: √2</p><p>&nbsp;</p><p>Asumsikan soal:</p><p>Hasil dari (sin 270° x cos 135° + tan 135°)/(sin 150° + sin 225°) adalah ....</p><p>&nbsp;</p><p>Konsep:</p><p>sin 270° = −1</p><p>tan 135° = −1</p><p>cos (90° + A) = −sin &nbsp;A</p><p>sin (90° + A) = cos A</p><p>sin (180° + A) = −sin A</p><p>&nbsp;</p><p>Pembahasan:</p><p>(sin 270° × cos 135° + tan 135°)/(sin 150° + sin 225°)</p><p>= ((−1) × cos (90° + 45°) + (−1))/(sin (90° + 60°) + sin (180° + 45°))</p><p>= ((−1) × (−sin 45°) + (−1))/(cos 60° + (−sin 45°))</p><p>= ((−1) × (−(1/2 √2)) + (−1))/(1/2 + (−(1/2 √2)))</p><p>= ((1/2) √2 − 1)/(1/2 − (1/2) √2)</p><p>= (√2/2 − 2/2)/(1/2 − √2/2)</p><p>= ((√2 − 2)/2)/((1 − √2)/2)</p><p>= (√2 − 2)/(1 − √2)</p><p>= ((√2 − 2)/(1 − √2)) × ((1 + √2)/(1 + √2))&nbsp;</p><p>= ((√2 − 2)(1 + √2))/((1 − √2)(1 + √2)) &nbsp;</p><p>= (√2 + 2 − 2 − 2√2)/((1² − (√2)²)</p><p>= (−√2)/(1 − 2)</p><p>= (−√2)/(−1)</p><p>= √2</p><p>&nbsp;</p><p>Jadi, hasilnya adalah √2.</p>