sec x is equal to 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
The Trigonometric Identities are equations that are true for Right Angled Triangles Periodicity of trig functions Sine cosine secant and cosecant have period 2 while tangent and cotangent have period Identities for negative angles Sine tangent cotangent and cosecant are odd functions while cosine and secant are even functions See below Use the identity sec x 1 cos x 1 secx 1 1 cosx 1 cosx 1 cos x
sec x is equal to
sec x is equal to
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Trigonometry Sec X Tan X M Find Sin X Multiple Choice Identity
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Sec x Sec A Sec theta Identity For Sec x Value Of Sec
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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 So we re looking for a way to represent secx tanx in terms of a tangent function with the input manipulated Let s start by looking at this rule tan a b tana tanb 1 tanatanb We ll need this later so it s important to be able to recognize if an expression of this form comes up cos 2x cos2x sin2x tan 2x 2tanx 1 tan2x
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 can rearrange the STEP 1 sec x 1 cos x STEP 2 Use the quotient rule to find the derivative of Sec x 1 cos x d dx 1 cos x d dx cosx 1 cosx 2
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Recall the definition of secx in terms of ratios of sides of a right angled triangle secx hyp adj hypotenuse divided by adjacent sides Consider a triangle with other angles both 45 o The two sides adjoining the right angle are of equal length call it a Pythagoras Theorem tells us that the hypotenuse is of length sqrt a 2 a 2 asqrt2 So 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
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How Do You Prove sec x Csc x 1 Tan x Csc x Socratic
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