what is sec equal to 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 1 cos 2x cos 2x sin 2x cos 2x 1 cos 2x 1 tan 2x sec 2x From this identity we
Here are a few examples I have prepared a Simplify tanx cscx xx secx Apply the quotient identity tantheta sintheta costheta and the reciprocal identities csctheta 1 sintheta and sectheta 1 costheta sinx cosx 1 sinx xx 1 cosx sinx cosx xx Trigonometric identities are equations involving the trigonometric functions that are true for every value of the variables involved Each of the six trig functions is equal to its co function evaluated at the complementary angle The Trigonometric Identities are equations that are true for Right Angled Triangles Periodicity of trig functions
what is sec equal to
what is sec equal to
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Explanation Let s use the definitions of secx and tanx to simplify this We know secx 1 cosx and tanx sinx cosx Let s plug these values into our original expression we get 1 cosx sinx cosx 1 cosx sinx cosx 1 sinx cscx Therefore secx tanx cscx Hope this helps Since the ranges are similar we can find x using x cos 1 1 2 3 sec 1 2 pi 3 Let the answer be x Since sec 1 2 x sec x 2 As secant is the reciprocal of the cosine function i e sec x 1 cos x the following must be true as well 1 cos x 2 Or cos x 1 2 The range of sec 1 x is 0 pi 2 uu
Explanation Use the identity secx 1 cosx 1 secx 1 1 cosx 1 cosx 1 cosx Answer link iOS 1 tan 2 x sec 2 x Answer link Related questions What does it mean to prove a trigonometric identity
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Secx 1 cosx We know d dx cosx sinx keep that in mind because we re going to need it Our problem is d dx secx Since secx 1 cosx we can write this as d dx 1 cosx We can find this derivative using the quotient rule d dx u v u v uv v2 In our case u 1 u 0 and v cosx v sinx Answer link sec x 1 cos x sec x You probably meant simplify The secant function is only the inverse of the cosine function So sec x 1 cos x Now the cosine function is said to be an even function That is if you put x instead of x you still get the same thing So cos x cos x Therefore sec x 1 cos x 1 cos
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what is sec equal to - Since the ranges are similar we can find x using x cos 1 1 2 3 sec 1 2 pi 3 Let the answer be x Since sec 1 2 x sec x 2 As secant is the reciprocal of the cosine function i e sec x 1 cos x the following must be true as well 1 cos x 2 Or cos x 1 2 The range of sec 1 x is 0 pi 2 uu