Question #ae3a2

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Answer 1 · 2017-09-26T15:14:20

1

tan(90-45)=tan45.

$tan θ = \frac{sin θ}{cos θ}$ $tan theta=(sin theta)/(cos theta)$

$tan 45 = \frac{sin 45}{cos 45}$ $tan 45 =(sin 45)/cos 45$

$sin 45 = cos 45 = \frac{1}{\sqrt{2}}$ $sin 45=cos 45=1/sqrt2$

Therefore

$tan 45 = \frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}$ $tan 45=(1/sqrt2)/(1/sqrt(2))$

$tan (90 - 45) = tan 45 = 1$ $tan(90-45)=tan 45=1$