Question

Root3tantheta - sectheta = 1 then find the value of theta

Answer 1

➼ Answer ➼

$\sqrt{3} tan\theta-sec\theta=1$

$=>\sqrt{3} \frac{sin\theta}{cos\theta} -\frac{1}{cos\theta} =1$

$=>\sqrt{3} \frac{sin\theta-1}{cos\theta} =1$

$=>\sqrt{3} sin\theta-1=cos\theta$

$=>\sqrt{3} sin\theta=1+cos\theta$

$=>3sin^{2}\theta=(1+cos\theta)^{2}$

$=>3sin^{2}\theta=1+cos^{2}\theta+2cos\theta$

$=>3(1-cos^{2}\theta)=1+cos^{2}\theta+2cos\theta$

$=>-3+3cos^{2}\theta+1+cos^{2}\theta+2cos\theta=0$

$=>4cos^{2}\theta+2cos\theta-2=0$

Quadratic Equation:

$=>\frac{-2+-\sqrt{2^{2}-4*4*(-2)} }{2*4}$

$=>\frac{-2+-\sqrt{4-4*(-8)} }{8}$

$=>\frac{-2+-\sqrt{4+32} }{8}$

$=>\frac{-2+-\sqrt{36} }{8}$

$=>\frac{-2+-6}{8}$

Hence,

$cos\theta =\frac{-2+6 }{8}$

$=\frac{4}{8}$

$=\frac{1 }{2}$

$cos\theta=\frac{-2-6 }{8}$

$=\frac{-8}{8}$

$=-1$

Thus,

$\theta=60$°

$\theta=180$°

☆ Hope it Helps ☆

$@NightRead$