Prove that: (sin 20 -sin 10) / 1- cos 10 + cos 20 = tan 10
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Step-by-step explanation:
cos20 = cos²10 - sin²10
1 = cos²10 + sin²10
sin20 = 2sin10cos10
Substitute the above in equation
=> (sin20 - sin10)/(cos²10 + sin²10 - cos10 + cos²10 - sin²10)
=> (sin20 - sin10)/(2cos²10 - cos10)
=> (2sin10cos10 - sin10)/[cos10(2cos10 - 1)]
=> [sin10(2cos10 -1)]/[cos10(2cos10 - 1)]
=> sin10/cos10 = tan10
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