solve-cosx-3-sinx-1-

Question Number 78946 by mathocean1 last updated on 21/Jan/20

solve

\cos x - \sqrt{3} s i n x = 1

Commented by msup trace by abdo last updated on 21/Jan/20

e \Leftrightarrow 2 (\frac{1}{2} c o s x - \frac{\sqrt{3}}{2} s i n x) = 1 \Rightarrow

c o s (\frac{π}{3}) c o s x - s i n (\frac{π}{3}) s i n x = \frac{1}{2}

\Rightarrow c o s (x + \frac{π}{3}) = c o s (\frac{π}{3}) \Rightarrow

x + \frac{π}{3} = \frac{π}{3} + 2 k π o r x + \frac{π}{3} = \frac{2 π}{3} + 2 k π (k f r o m Z)

\Rightarrow x = 3 k π o r = \frac{π}{3} + 2 k π

Commented by msup trace by abdo last updated on 21/Jan/20

e r r o r o f t y p o x = 2 k π o r x = \frac{π}{3} + 2 k π

Answered by Mr. AR last updated on 31/Jan/20

c o s (90 ° - x) - \sqrt{3} s i n x = 1

s i n x - \sqrt{3} s i n x = 1

s i n x (1 - \sqrt{3}) = 1

s i n x = \frac{1}{1 - \sqrt{3}} \times \frac{1 + \sqrt{3}}{1 + \sqrt{3}}

s i n x = \frac{1 + 1.732}{1 - 3}

s i n x = \frac{2.732}{- 2}

s i n x = - 1.366

Facebook Tweet Pin