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Verify the trig identity 1/tan + tan= sec^2/ tan[tex] \tan( \sec - \frac{\pi}{4} ) = \frac{ \tan( \sec( - 1) ) }{1 + \tan( \sec(?) ) } [/tex]

Sagot :

Starting with the equation:

[tex]\frac{1}{\tan(x)}+\tan (x)=\frac{\sec ^2(x)}{\tan (x)}[/tex]

Take the expression on the right hand side of the equation:

[tex]\frac{\sec ^2(x)}{\tan (x)}[/tex]

From the Pythagorean Identity and the definition of secant, we can prove that:

[tex]1+\tan ^2(x)=\sec ^2(x)[/tex]

That fact can be verified as follows: the Pythagorean Identity states that:

[tex]\sin ^2(x)+\cos ^2(x)=1[/tex]

Divide both sides by the squared sine of x:

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