Question

if sinα + sinβ = 2
then find the value of
cos²α + cos²β​

Answer 1

${\large{\bold{\rm{\underline{Given \; that}}}}}$

${\sf{\bigstar \: sin \alpha \: + sin \beta \: = 2}}$

${\large{\bold{\rm{\underline{To \; find}}}}}$

${\sf{\bigstar \: cos^{2} \alpha \: + cos^{2} \beta}}$

${\large{\bold{\rm{\underline{Solution}}}}}$

${\sf{\bigstar \: cos^{2} \alpha \: + cos^{2} \beta \: = 0}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

As it's given that.

$</p><p>{\red{sin \alpha \: + sin \beta \: = 2}}$

Henceforth,

${\sf{:\implies \: sin \alpha \: = 2}}$

${\sf{:\implies \: sin \beta \: = 2}}$

~ That's why,

${\sf{:\implies \: sin \alpha \: = 90 \degree}}$

${\sf{:\implies \: sin \beta \: = 90 \degree}}$

~Putting the Values,

${\sf{:\implies \: sin(90 \degree) + \: sin(90 \degree)}}$

${\sf{:\implies \: 1 + 1}}$

${\sf{:\implies \: 2}}$

~As we know that we have to find

${\purple{cos^{2} \alpha \: + cos^{2} \beta}}$

Let's Put the values

${\sf{\implies \: cos^{2}(90 \degree) \: + cos^{2} (90 \degree)}}$

${\sf{\implies \: 0}}$