Question

Cos10°-cos50°= sin20° prove that

Answer 1

Answer:

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Step-by-step explanation:

$to \: provv = \\ cos \: 10 - cos \: 50 = sin \: 20 \\ \\ let \: then \\ \: LHS = cos \: 10 - cos \: 50 \\ RHS = sin \: 20$

$considering \: first \: LHS \\ = cos \: 10 - cos \: 50 \\ \\ = cos \: (30 - 20) - cos \: (30 + 20) \\ \\ we \: know \: that \\ cos \: (x + y) = cos \: x.cos \: y - sin \: x.sin \: y \\ \\ cos \: (x - y) = cos \: x.cos \: y + sin \: x.sin \: y \\ \\ hence \: accordingly \\ = cos \: 30.cos \: 20 + sin \: 30.sin \: 20 \: - \: (cos \: 30.cos \: 20 - sin \: 30.sin \: 20) \\ \\ = cos \: 30.cos \: 20 + sin \: 30.sin \: 20 \: - cos \: 30.cos \: 20 + sin \: 30.sin \: 20 \\ \\ = sin \: 30.sin \: 20 + sin \: 30.sin \: 20 \\ \\ = 2.sin \: 30.sin \: 20 \\ \\ = 2 \times \frac{1}{2} \times sin \: 20 \\ \\ = sin \: 20$

$hence \: then \\ LHS = RHS \\ \\ thus \: proved$