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Question

If tanα=17 and sinβ=110
where 0<α,β<π2, then 2β is equal to

A
π4α
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B
3π4α
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C
π8α2
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D
3π8α2
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Solution

The correct option is A π4α

sinβ=110tanβ=13tan2β=2tanβ1tan2β=2.13119=34tanα=17tan(α+2β)=tanα+tan2β1tanαtan2β=17+34117.34=1
α+2β=π42β=π4α


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