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

The given equation may be written as 2/cos 2α=sin β/cos β+cos β/sin β=sin^2 β+cos^2 β/cos β sin β=1/cos β. sin β ⇒ cos 2α=sin 2β ⇒ cos 2α=cos (π/2 2β)⇒ 2α=π/2 2 ...

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Standard XIII

Mathematics

Trigonometric Ratios of Multiples of an Angle

If 2 sec 2α=t...

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

\frac{π}{4}

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\frac{π}{2}

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π

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2 π

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Solution

The correct option is A $\frac{π}{4}$
The given equation may be written as
$\frac{2}{c o s 2 α} = \frac{s i n β}{c o s β} + \frac{c o s β}{s i n β} = \frac{s i n^{2} β + c o s^{2} β}{c o s β s i n β} = \frac{1}{c o s β . s i n β}$
$\Rightarrow c o s 2 α = s i n 2 β$
$\Rightarrow c o s 2 α = c o s (\frac{π}{2} - 2 β) \Rightarrow 2 α = \frac{π}{2} - 2 β$
$\Rightarrow 2 α + 2 β = \frac{π}{2} \Rightarrow α + β = \frac{π}{4} .$

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If 2 sec 2α=tan β+cot β, then one of the values of α+β is

The correct option is A π4The given equation may be written as 2cos 2α=sin βcos β+cos βsin β=sin2 β+cos2 βcos β sin β=1cos β. sin β ⇒cos 2α=sin 2β ⇒cos 2α=cos(π2−2β)⇒2α=π2−2β ⇒2α+2β=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