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Question

Let cos(α+β)=45 and let sin(αβ)=513 where 0α,βπ4, then tan2α=

A
2516
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B
5633
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C
1912
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D
207
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Solution

The correct option is B 5633
cos(α+β)=45 sin(αβ)=513
sin(α+β)=35 cos(αβ)=1213

sin(α+β)+sin(αβ)=2sinαcosβ

513+35=6465

cos(α+β)+cos(αβ)=2cosαcosβ

=45+213=11265

2sinαcosβ2cosαcosβ=tanα=646511265=47

tan(2α)=2tan(α)1tan2(α)=2×4711649

tan(2α)=873349=5633.

1331272_1226846_ans_3dcc3e75cc7547d68effeb3ab4730c09.JPG

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