Let A1-2-Bcosec -2 and C2- are 3 points such that OA2-OB-OC-O is the origin then the value of 2sin2-tan2- is

Given : (OA)^2=OB·OC ⇒ 5=√(cosec^2 α+4)·√(4+^2β) ⇒ (cosec^2 α+4)(^2β+4)=25 only possible condition is : cosec^2α+4=^2β+4=5 ⇒ cosec^2α=^2β=1 sin^2α=cos^2β=1 ∴ 2s ...

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Standard XI

Mathematics

Rectangular Cartesian Coordinate System

Let A1,2,Bcos...

Question

Let $A (1, 2), B (cosec α, - 2)$ and $C (2, sec β)$ are $3$ points such that $(O A)^{2} = O B \cdot O C$ ,( $O$ is the origin) then the value of $2 {sin}^{2} α - {tan}^{2} β$ is

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Solution

The correct option is B $2$
Given : $(O A)^{2} = O B \cdot O C \Rightarrow 5 = \sqrt{{cosec}^{2} α + 4} \cdot \sqrt{4 + {sec}^{2} β}$
$\Rightarrow ({cosec}^{2} α + 4) ({sec}^{2} β + 4) = 25$
only possible condition is : ${cosec}^{2} α + 4 = {sec}^{2} β + 4 = 5$
$\Rightarrow {cosec}^{2} α = {sec}^{2} β = 1$
${sin}^{2} α = {cos}^{2} β = 1$
$∴ 2 {sin}^{2} α - {tan}^{2} β = 2$

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Let A(1,2),B(cosec α,−2) and C(2,secβ) are 3 points such that (OA)2=OB⋅OC,(O is the origin) then the value of 2sin2α−tan2β is

The correct option is B 2Given : (OA)2=OB⋅OC ⇒ 5=√cosec2 α+4⋅√4+sec2β ⇒ (cosec2 α+4)(sec2β+4)=25 only possible condition is : cosec2α+4=sec2β+4=5 ⇒ cosec2α=sec2β=1 sin2α=cos2β=1 ∴ 2sin2α−tan2β=2

Let $A (1, 2), B (cosec α, - 2)$ and $C (2, sec β)$ are $3$ points such that $(O A)^{2} = O B \cdot O C$ ,( $O$ is the origin) then the value of $2 {sin}^{2} α - {tan}^{2} β$ is