Let sin-1237 for -2- - and cos- - 20101 for -3 -2-2 - If cosec - - -pq where p and q are co-prime numbers- then the value of p-q is

Cosα =√(1 sin^2 α)= 3537 [∵α∈(π2, π)] and sinβ = √(1 cos^2 β)= 99101 [∵β∈(3π2, 2π)] Now, nbsp;sin(α+β) =sinαcosβ+cosαsinβ =1237×20101+3537×99101 =370 ...

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Byju's Answer

Standard XII

Mathematics

Graph of Trigonometric Ratios

Let sinα=1237...

Question

Let $sin α = \frac{12}{37}$ for $α \in (\frac{π}{2}, π)$ and $cos β = \frac{20}{101}$ for $β \in (\frac{3 π}{2}, 2 π) .$ If $cosec (α + β) = \frac{p}{q}$ where $p$ and $q$ are co-prime numbers, then the value of $p + q$ is

7442

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Solution

The correct option is A $7442$
$cos α = \sqrt{1 - {sin}^{2} α} = - \frac{35}{37} [∵ α \in (\frac{π}{2}, π)]$
and $sin β = \sqrt{1 - {cos}^{2} β} = - \frac{99}{101} [∵ β \in (\frac{3 π}{2}, 2 π)]$

Now, $sin (α + β)$
$= sin α cos β + cos α sin β$
$= \frac{12}{37} \times \frac{20}{101} + \frac{35}{37} \times \frac{99}{101}$
$= \frac{3705}{3737} = \frac{p}{q}$
$∴ p + q = 7442$

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Let sinα=1237 for α∈(π2,π) and cosβ=20101 for β∈(3π2,2π). If cosec (α+β)=pq where p and q are co-prime numbers, then the value of p+q is

The correct option is A 7442cosα=√1−sin2α=−3537 [∵α∈(π2,π)] and sinβ=√1−cos2β=−99101 [∵β∈(3π2,2π)] Now, sin(α+β) =sinαcosβ+cosαsinβ =1237×20101+3537×99101 =37053737=pq ∴p+q=7442

Let $sin α = \frac{12}{37}$ for $α \in (\frac{π}{2}, π)$ and $cos β = \frac{20}{101}$ for $β \in (\frac{3 π}{2}, 2 π) .$ If $cosec (α + β) = \frac{p}{q}$ where $p$ and $q$ are co-prime numbers, then the value of $p + q$ is