What are the solution in the interval [0, 2pie]? sec^2x-tan^2x=0

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Answer 1 · 2018-04-04T07:41:40

See explanation

We want to solve the equation

#sec^2(x)-tan^2(x)=0#

To get a better idea, write this in terms of sine and cosine

#1/cos^2(x)-sin^2(x)/cos^2(x)=0#

To simplify multiply both sides by #cos^2(x)#

#1-sin^2(x)=0#

Thus

#sin^2(x)=1#

#=>sin(x)=+-sqrt(1)#

#=>sin(x)=+-1#

Now i will leave it for you to find the solutions