Question

$sin^{2} \alpha + 7 \cos ^{2} \alpha = 4 \\ then the \: value \: of \: tan \alpha \: is \: (where \: 0 ^0 \: < \: \alpha \: < 90 ^0)$
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Answer 1

$heya \\ \\ \\ \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) + 6 \cos {}^{2} ( \alpha ) = 4 \\ \\ \\ \\ \\ 6 \cos {}^{2} ( \alpha ) + 1 = 4 \\ \\ \\ \\ \\ \cos {}^{2} ( \alpha ) = 1 \div 2 \\ \\ \\ \\ \cos( \alpha ) = \cos(60) \\ \\ \\ \alpha = 60 \\ \\ \\ \\ or \\ \\ \\ \\ \cos( \alpha ) = - 1 \div 2 \\ \\ \\ \\ \cos( \alpha ) = \cos(120) \\ \\ \\ \ = 120 \\ \\ \\ \alpha = 120 \: \: \: will \: be \: \: rejected \: becoz \: \alpha < 90 \\ \\ \\ \\ \alpha = 60 \\ \\ \\ \\ \\ tan( \alpha ) = tan(60) = \sqrt{3}$