If $sin α = \frac{4}{5}$ $sin alpha = 4/5$ and $cos β = \frac{4}{5}$ $cos beta = 4/5$ , So which of the following is true? (Options Below)

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If $sin α = \frac{4}{5}$ $sin alpha = 4/5$ and $cos β = \frac{4}{5}$ $cos beta = 4/5$ , So which of the following is true? (Options Below)

a) $α < β$ $alpha ltbeta$

b) $α > β$ $alpha gt beta$

c) $α = β$ $alpha = beta$

d)None of the Above

1 Answer

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Answer 1 · 2018-03-11T04:06:26

See the answer below...

Explanation:

$sin α = \frac{4}{5}$ $sin alpha=4/5$

$cos β = \frac{4}{5} \Rightarrow sin β = \frac{3}{5}$ $cosbeta=4/5" "=>" "sinbeta=3/5$

$\Rightarrow {cos}^{2} β = \frac{16}{25}$ $=>cos^2beta=16/25$

$\Rightarrow 1 - {sin}^{2} β = \frac{16}{25}$ $=>1-sin^2beta=16/25$

$\Rightarrow {sin}^{2} β = \frac{9}{25}$ $=>sin^2beta=9/25$

$\Rightarrow sin β = \frac{3}{5}$ $=>sin beta=3/5$

$\frac{3}{5} < \frac{4}{5}$ $color(red)(3/5<4/5$
$\Rightarrow sin β < sin α$ $=>sin beta < sin alpha$
$=>color(red)(ul(bar(|color(green)(beta < alpha))|$

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If $sin α = \frac{4}{5}$ $sin alpha = 4/5$ and $cos β = \frac{4}{5}$ $cos beta = 4/5$ , So which of the following is true? (Options Below)

a) $α < β$ $alpha ltbeta$

b) $α > β$ $alpha gt beta$

c) $α = β$ $alpha = beta$

d)None of the Above

1 Answer

Explanation:

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If sin alpha = 4/5sinα=45sin alpha = 4/5 and cos beta = 4/5cosβ=45cos beta = 4/5, So which of the following is true? (Options Below)

a)alpha ltbetaα<βalpha ltbeta b)alpha gt betaα>βalpha gt beta c)alpha = betaα=βalpha = beta d)None of the Above

1 Answer

Explanation:

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Impact of this question

If $sin α = \frac{4}{5}$ $sin alpha = 4/5$ and $cos β = \frac{4}{5}$ $cos beta = 4/5$ , So which of the following is true? (Options Below)

a) $α < β$ $alpha ltbeta$

b) $α > β$ $alpha gt beta$

c) $α = β$ $alpha = beta$

d)None of the Above