If - and - are two positive acute angles satisfying - - 150 and sin- - cos 2- then the value of - - - is equal to

The correct option is C 65^o sinα=cos(2β) Or #160; sin(α)=cos(2α 30^0) Or #160; cos(90^0 α)=cos(2α 30^0) Or #160; 90^0 α=2α 30^0 Or ...

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Standard XII

Mathematics

Strictly Increasing Functions

If α and ...

Question

If $α$ and $β$ are two positive acute angles satisfying $α - β = 15^{0}$ and $sin α = cos 2 β$ then the value of $α + β$ is equal to

35^{o}

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55^{o}

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65^{o}

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85^{o}

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Solution

The correct option is C $65^{o}$
$sin α = cos (2 β)$
Or
$sin (α) = cos (2 α - 30^{0})$
Or
$cos (90^{0} - α) = cos (2 α - 30^{0})$
Or
$90^{0} - α = 2 α - 30^{0}$
Or
$120^{0} = 3 α$
Or
$α = 40^{0}$
Hence
$β = 25^{0}$ .
Therefore $α + β = 65^{0}$

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If α and β are two positive acute angles satisfying α−β=150 and sinα=cos2β then the value of α+β is equal to

The correct option is C 65osinα=cos(2β)Or sin(α)=cos(2α−300)Or cos(900−α)=cos(2α−300)Or 900−α=2α−300Or 1200=3αOr α=400Henceβ=250.Therefore α+β=650

If $α$ and $β$ are two positive acute angles satisfying $α - β = 15^{0}$ and $sin α = cos 2 β$ then the value of $α + β$ is equal to

The correct option is C $65^{o}$
$sin α = cos (2 β)$
Or
$sin (α) = cos (2 α - 30^{0})$
Or
$cos (90^{0} - α) = cos (2 α - 30^{0})$
Or
$90^{0} - α = 2 α - 30^{0}$
Or
$120^{0} = 3 α$
Or
$α = 40^{0}$
Hence
$β = 25^{0}$ .
Therefore $α + β = 65^{0}$