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Question

If 0<β<α<π4,cos(α+β)=35 and cos(αβ)=45 then sin2α is equal to

A
1
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B
0
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C
2
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D
none of these
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Solution

The correct option is A 1
cos(α+β)=35sin(α+β)=45

cos(αβ)=45sin(αβ)=35

sin(α+β)+sin(αβ)cos(α+β)+cos(αβ)=45+3535+45

2sinαcosβ2cosαcosβ=1tanα=1

sin2α=2tanα1+tan2α=21+1=1

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