Use trigonometric identities, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0,2π).

Question

Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." −15sec2(x)+17=tan(x)

Answer 1

Doug does such a great job with using sec²x=tan²x+1 identity

but at 15tan²x+tanx-2=0

you can use quadradic root formula

to find either tanx= -2/5 or tanx=1/3

Answer 2

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