express cos30°×sin20° as the sum or difference
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Answer:
cos30 × sin20 = [cos^2 30.sin10] - [sin30.cos30.cos10]
Step-by-step explanation:
cos30 × sin20
= cos30 × sin(90-70)
= cos30 × cos70 ---------[ sin(90-A) = cosA ]
= cos30 × cos(60+10)
= cos30 × {sin60.sin10 - cos60.cos10}
---------[ cos(A +B) = sinA.sinB - cosA.cosB ]
= cos30.sin60.sin10 - cos60.cos10.cos30
= cos30.cos30.sin10 - sin30.cos30.cos10
---------[ sin(90-A) = cosA ; cos(90-A) = sinA ]
= cos^2 30.sin10 - sin30.cos30.cos10
so,
cos30 × sin20 = [cos^2 30.sin10] - [sin30.cos30.cos10]
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