If 2 2 -tan-then one of the values of - is

The correct option is C 2 sec (2α)=tan β +cotβ=tan β +1/tan β=2 ( 1+tan^2 β/2 tan β )=2cosec(2β) ⇒ cos 2α=sin 2β =cos ( π/2 2 β )⇒ 2α =π/2 2 β⇒ 2(α +β)=π/2⇒α ...

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Standard XI

Mathematics

Sin(A+B)Sin(A-B)

If 2 2 α=tanβ...

Question

If $2 s e c (2 α) = t a n β + c o t β$ ,then one of the values of $α + β$ is

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Solution

The correct option is C
$2 s e c (2 α) = t a n β + c o t β = t a n β + \frac{1}{t a n β} = 2 (\frac{1 + t a n^{2} β}{2 t a n β}) = 2 c o s e c (2 β) \Rightarrow c o s 2 α = s i n 2 β = c o s (\frac{π}{2} - 2 β) \Rightarrow 2 α = \frac{π}{2} - 2 β \Rightarrow 2 (α + β) = \frac{π}{2} \Rightarrow α + β = \frac{π}{4}$

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If 2sec(2α)=tanβ+cotβ ,then one of the values of α+βis

The correct option is C 2sec(2α)=tanβ+cotβ=tanβ+1tanβ=2(1+tan2β2tanβ)=2cosec(2β)⇒cos2α=sin2β=cos(π2−2β)⇒2α=π2−2β⇒2(α+β)=π2⇒α+β=π4

If $2 s e c (2 α) = t a n β + c o t β$ ,then one of the values of $α + β$ is