Question

$if \: \sin(a) \: + \: \cos(a) \: = \: \sqrt{2 }cos(a) \: then \: the \: value \: of \: \tan(a) \: is \\ \\ (a) \: \sqrt{2} - 1 \\ (b) \: \sqrt{2} + 1 \\ (c) \: \sqrt{2} \\ (d) \: - \sqrt{2}$
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Answer 1

Answer:

Hey,

There your answer

$Since \: \\ \: \: \: \: \: \: \: TanA = \frac{sina}{cosa} \\ \: \: => SinA = TanA \times CosA \\ \\ Now \\ \: \: \: A/q \\ \: \: \: \: SinA \: + CosA = \sqrt{2} CosA \\ => TanA.CosA + CosA= \sqrt{2} CosA \\ => CosA(TanA + 1) = \sqrt{2} CosA \\ => TanA + 1 = \sqrt{2} \\ => TanA= \sqrt{2} - 1$

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