If tan -1-cos-sin- then

The correct option is B tan 2 α = tan β tan 2 α = tan β tan α =1 cos β/sin β =2 sin^2 β/2/2 sin β/2 cos β/2 =sin β/2/cos β/2 ⇒ tan α = tan β/2 ⇒ α =β/2 ⇒ ...

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Standard XII

Mathematics

Trigonometric Equations

If tan α=1-co...

Question

If $t a n α = \frac{1 - c o s β}{s i n β}$ , then

$t a n 3 α = t a n 2 β$

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$t a n 2 α = t a n β$

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$t a n 2 β = t a n α$

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none of these

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Solution

The correct option is B
$t a n 2 α = t a n β$

$t a n 2 α = t a n β$

$t a n α = \frac{1 - c o s β}{s i n β} = \frac{2 s i n^{2} \frac{β}{2}}{2 s i n \frac{β}{2} c o s \frac{β}{2}} = \frac{s i n \frac{β}{2}}{c o s \frac{β}{2}} \Rightarrow t a n α = t a n \frac{β}{2} \Rightarrow α = \frac{β}{2} \Rightarrow 2 α = β ∴ t a n 2 α = t a n β$

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Similar questions

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If tan α=1−cos βsin β, then

The correct option is B tan 2α=tan β tan 2α=tan β tan α=1−cos βsin β=2 sin2 β22 sin β2 cos β2=sinβ2cosβ2⇒ tan α=tan β2⇒ α=β2⇒ 2α=β∴ tan 2α=tanβ

If $t a n α = \frac{1 - c o s β}{s i n β}$ , then