Question

If sinA/cosA=√2cosA,find tanA and cotA​

Answer 1

Step-by-step explanation:

sinA/cosA=tanA

so,tanA=root2cosA

cotA=1/tanA

=1/root2cosA

Answer 2

Answer:

$\frac{ \sin(x) }{ \cos(x) } = \sqrt{2} \cos(x) \\ \\ \sin(x) = \sqrt{2} \cos {}^{2} (x) = \sqrt{2} (1 - \sin {}^{2} (x) ) \\ \sqrt{2} \sin {}^{2} (x) + \sin(x) - \sqrt{2} = 0 \\ let \: \: \sin(x) = y ,\: y\in [-1,1] \\ \sqrt{2} \: {y}^{2} + y - \sqrt{2} = 0 \\\\ y = \frac{ - 1 \pm \sqrt{1 + 8} }{ \sqrt{2} } = \frac{1}{ \sqrt{2} } \\ \\ \sin(x) = \frac{1}{ \sqrt{2} } \implies \: x = 45 \\ \cos(45) = \frac{1}{ \sqrt{2} } \: \: an d \: \: \: \: \tan(x) = 1$