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# please solve the following equation using trig

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(you cant see this on the front page because it's in LaTeX)

$$x+\frac{x}{\sqrt{x^2-1}}=\frac{35}{12}$$ thank you soo muchhh

p.s. i was given the following hint but i dont know how to incorporate it $$Let x=\frac{1}{cos\alpha}$$ with $$\alpha \epsilon(0, \frac{\pi}{2})$$

Apr 6, 2019

$$\text{Consider a triangle with legs }s_1=1,~s_2 = \sqrt{x^2-1}\\ \text{You end up with the equation}\\ \sec(\alpha) + \csc(\alpha) = \dfrac{35}{12}\\ \text{which can be solved with some annoying algebra}$$