Question

if sin alpha+sin beta=2, then the value of cos^2alpha+cos^2 beta?

Answer 1

$\red {\large\tt{\underline { \underline {\star \: {Given:-}}}}}$

$\sin \alpha + \sin \beta = 2. \\ \star \: \: \: Then \: find \: the \: value \: of \\ {\cos }^{2} \alpha + { \cos }^{2} \beta =$

$\red {\large\tt{\underline { \underline {\star \: {Solution:-}}}}}$

$\sin \alpha + \sin \beta = 2. \\ \\ \implies \sin90 \degree + \sin90 \degree = 2. \\ \\ \implies 1 + 1 = 2.$

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Now,

According to questions.

${ \cos }^{2} \alpha + { \cos }^{2} \beta . \\ \\ \implies{(90) \degree }^{2} +{ 90 \degree }^{2} . \\ \\ \implies {0}^{2} + {0}^{2} . \\ \\ \implies 0.$

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$\red {\large\tt{\underline { \underline {\star \: {Some \: \: information:-}}}}}$

$\sin\alpha + \sin \beta = 2.$

# It will be possible when.

$\alpha = 90 \degree$

$\beta = 90 \degree$

$\sin90 = 1$

$\cos90 = 0.$