sec 2 x identity

sec 2 x identity Answer link You can reuse this answer See Below Left Hand Side sec 2 x tan 2x 1 cos 2x sin 2x cos 2x 1 sin 2x cos 2x cos 2x cos 2x Use Property sin 2x cos 2x 1 and isolate cos 2x cancel cos 2x cos 2x 1 Right Hand Side

If you forget these just remember how to derive them by dividing by either cos2x or sin2x Using the Pythagorean identity tan 2x sec 2x 1 This is an application of the Pythagorean identities namely 1 tan 2x sec 2x This can be derived from the standard Pythagorean identity by dividing everything by cos 2x like so cos 2x sin 2x Divide all terms on both sides by cos2x sin2x cos2x cos2x cos2x 1 cos2x Reminder a a tanx sinx cosx and secx 1 cosx a a

sec 2 x identity

sec 2 x identity
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Verifying A Trigonometric Identity Sin 2 x cos x Sec x Cos x
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Tan 2 Sec 2 Identity 110509 Tan 2 Sec 2 Identity
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Divide both sides by cos2 x to get cos2 x cos2 x sin2 x cos2 x 1 cos2 x which simplifies to 1 tan2 x sec2 x See explanation Starting from cos 2 x sin 2 x 1 Divide both sides by cos 2 x to get cos 2 x cos 2 x sin 2 x cos 2 x 1 cos 2 x which simplifies to 1 tan 2 x sec 2 x Note that sin 2 x cos 2 x 1 Hence cos 2 x 1 sin 2 x and we find sec 2 x tan 2 x 1 cos 2 x sin 2 x cos 2 x

Explanation sec2x 1 cos2x 1 cos2x sin2x using double angle formula 1 1 sec2x 1 csc2x 1 csc2x sec2x sec2xcsc 2x sec2x csc2x csc2x sec2x See Below sec 2x 1 cos 2x 1 cos x x 1 cos x cos x sin x sin x Expanded using addition identity 1 1 sec x 1 secx 1 csc x 1 Begin from the color blue basic trigonometric identity color red bar ul color white a a color black sin 2x cos 2x 1 color white a a

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True Start with the well known pythagorean identity sin 2x cos 2x 1 This is readily derived directly from the definition of the basic trigonometric functions sin and cos and Pythagoras s Theorem Divide both side by cos 2x and we get sin 2x cos 2x cos 2x cos 2x 1 cos 2x tan 2x 1 sec 2x tan 2x sec 2x 1 Confirming that the result is an identity Required to prove sec 2 x 2 2secx 2 secx 2 cosx Right Hand Side 2secx 2 secx 2 cosx

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sec 2 x identity - Begin from the color blue basic trigonometric identity color red bar ul color white a a color black sin 2x cos 2x 1 color white a a