Question

sin a+cosa=√2,evaluate tana+cosa

Answer 1

$( \sin( \alpha ) + \cos( \alpha ) ) = \sqrt{2} \\ square \: both \: sides \\ {sin}^{2} \alpha + {cos}^{2} \alpha + 2 \sin( \alpha ) cos \alpha = 2 \\ 1 + 2 \sin( \alpha ) \cos( \alpha ) = 2 \\ 2 \sin( \alpha ) \cos( \alpha ) = 1 \\ sin2 \alpha = 1 \\ 2 \alpha = 9 0 \\ \alpha = 45$
therefore
$\tan( \alpha ) + \cos( \alpha ) \\ = \tan(45) + \cos(45) \\ = 1 + (1 \div \sqrt[]{2} ) \\ = ( \sqrt{2} + 1) \div ( \sqrt{2)}$
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