Question

can I guys pls solve these 2 questions it's very urgent ​

Answer 1

$lhs = \frac{ \cos(x) }{ \sin(90 - x) } + \frac{ \sin(x) }{ \cos(90 - x) } \\ \: \: \: \: \: \: \: = \frac{ \cos(x) }{ \cos(x) } + \frac{ \sin(x) }{ \sin(x) } = 1 + 1 = 2 = rhs$

$lhs = \sqrt{ \frac{(1 - \sin(x))(1 - \sin(x)) }{(1 - \sin {}^{2} (x)) } } \\ \: \: \: \: \: \: \: = \sqrt{ \frac{ {(1 - \sin(x)) }^{2} }{ \cos {}^{2} (x) } } = \frac{1 - \sin(x) }{ \cos(x) } \\ \: \: \: \: \: \: \: = \frac{1}{ \cos(x) } - \frac{ \sin(x) }{ \cos(x) } = \sec(x) - \tan(x)$

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