If sin x- cosec x- tan y- y-4- where x and y - -0- -2- then tany2 is a root of the equation-

The correct option is B α^2+2α 1=0 Using, A.M. gt;G.M. inequality, #160; L.H.S ≥ 4 Hence the equation #160;is true only #160;when x=π2, ...

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Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

If sin x+ c...

Question

If $sin x + c o s e c x + tan y + cot y = 4$ , where x and y $ϵ [0, \frac{π}{2}]$ , then $tan \frac{y}{2}$ is a root of the equation-

α^{2} + 2 α + 1 = 0

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α^{2} + 2 α - 1 = 0

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2 α^{2} - 2 α - 1 = 0

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α^{2} - α - 1 = 0

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Solution

The correct option is B $α^{2} + 2 α - 1 = 0$
Using, A.M. >G.M. inequality,
$L . H . S \geq 4$
Hence the equation is true only when $x = \frac{π}{2}, \frac{y π}{4}, tan y = 1$
$\Rightarrow \frac{2 tan \frac{y}{2}}{1 - {tan}^{2} \frac{y}{2}} = 1$
$\Rightarrow {tan}^{2} \frac{y}{2} + 2 tan \frac{y}{2} - 1 = 0$ .

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If sinx+cosecx+tany+coty=4, where x and y ϵ[0,π2], then tany2 is a root of the equation-

The correct option is B α2+2α−1=0Using, A.M. >G.M. inequality, L.H.S≥4Hence the equation is true only when x=π2,yπ4,tany=1⇒2tany21−tan2y2=1⇒tan2y2+2tany2−1=0.

If $sin x + c o s e c x + tan y + cot y = 4$ , where x and y $ϵ [0, \frac{π}{2}]$ , then $tan \frac{y}{2}$ is a root of the equation-