If sin 3-8 cos 3-1-6 sin-cos- where - -0- -2- thenthe value of - is

The correct option is D 5If we considersin^3α, 8cos^3β and 1 as 3 individual terms, then : A.M. = nbsp;sin^3α+8cos^3β+1/3 G.M.=√(sin^3α×8cos^3β×1)=2sinα ...

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Standard XII

Mathematics

AM,GM,HM Inequality

If sin 3α+8 c...

Question

$If {sin}^{3} α + 8 {cos}^{3} β + 1 = 6 sin α cos β where α, β \in [0, \frac{π}{2}], then the value of \frac{α + β}{α - β} is$

\frac{1}{2}

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Solution

The correct option is D $5$
$If we consider {sin}^{3} α, 8 {cos}^{3} β and 1 as 3 individual terms, then :- A . M . = \frac{{sin}^{3} α + 8 {cos}^{3} β + 1}{3} G . M . = \sqrt[3]{{sin}^{3} α \times 8 {cos}^{3} β \times 1} = 2 sin α cos β \Rightarrow A . M . = G . M . (Acc. to eqn. given. \Rightarrow All the individual terms are equal, \Rightarrow {sin}^{3} α = 1, 8 {cos}^{3} β = 1 \Rightarrow α = \frac{π}{2}, β = \frac{π}{3} \Rightarrow \frac{α + β}{α - β} = 5$

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If sin3α+8cos3β+1=6sinαcosβ where α,β∈[0,π2], then the value of α+βα−β is

The correct option is D 5If we considersin3α, 8cos3β and 1as 3 individual terms, then :-A.M.=sin3α+8cos3β+13G.M.=3√sin3α×8cos3β×1=2sinαcosβ ⇒A.M.=G.M. (Acc. to eqn. given.⇒ All the individual terms are equal,⇒sin3α=1, 8cos3β=1⇒α=π2, β=π3⇒α+βα−β=5

$If {sin}^{3} α + 8 {cos}^{3} β + 1 = 6 sin α cos β where α, β \in [0, \frac{π}{2}], then the value of \frac{α + β}{α - β} is$