Question

If A=45 degrees,B=30 degrees then find sinA/cosA+sinAsinB

Answer 1

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Answer 2

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a = 45°

b = 30°

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$\sin(a) = \sin(45) \\ \\ \sin(a) = \frac{1}{ \sqrt{2} }$

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$\cos(a) = \cos(45) \\ \\ \cos(a) = \frac{1}{ \sqrt{2} }$

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$\sin(b) = \sin(30) \\ \\ \sin(b) = \frac{1}{2}$

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$\frac{ \sin(a) }{ \cos(a) } + \sin(a) \times \sin(b) \\ \\ \frac{ \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } } + \frac{1}{ \sqrt{2} } \times \frac{1}{2}$
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$\\ \\ \frac{ 1 \times \sqrt{2} }{1 \times \sqrt{2} } + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ 1 + \frac{1}{ \sqrt{2 } \times 2} \\ \\ 1 \:+\: \frac{1}{2 \sqrt{2} }$

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$to \: rationalize \: the \: denominator : \\ \\ \frac{1}{2 \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ \frac{ \sqrt{2} }{2 \sqrt{2 \times {2} } } \\ \\ \frac{ \sqrt{2} }{2 \times 2} \\ \\ \frac{ \sqrt{2} }{4}$

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$\bold{so\:the\:answer\:is\:1\:+\frac{\sqrt{2}}{4}}$

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