is tan 2x sec 2x 1 an identity Prove the identity We know that sin 2 x cos 2 x 1 Divide the equation by cos 2 x sin 2 x cos 2 x cos 2 x cos 2 x 1 cos 2 x Since sin x cos x tan x and 1 cos x s e c x tan 2 x 1 s e c 2 x rearranging the terms sec 2 x 1 tan 2 x Hence tan 2 x sec 2 x 1 is an identity
Note that the three identities above all involve squaring and the number 1 You can see the Pythagorean Thereom relationship clearly if you consider the unit circle where the angle is t the opposite side is sin t y the adjacent side is cos t x and the hypotenuse is 1 Answer tan 2 x sec 2 x 1 is an identity We can proceed step by step to prove this Explanation From trigonometric identities sin 2 x cos 2 x 1 Dividing LHS and RHS of the above identity by cos 2 x we get sin 2 x cos 2 x cos 2 x cos 2 x 1 cos 2 x
is tan 2x sec 2x 1 an identity
is tan 2x sec 2x 1 an identity
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The formula for tan 2x are tan 2x sec 2x 1 tan 2 x sec 2 x 1 tan 2x sin 2x cos 2x tan 2 x sin 2 x cos 2 x tan 2x 1 cot 2x tan 2 x 1 cot 2 x What is the Difference Between tan2x and tan 2x Tan2x is a double angle trigonometric formula which gives the value of the tangent function for the compound angle 2x Prove tan 2 x sin 2 x tan 2 x sin 2 x prove cot 2x frac 1 tan 2 x 2 tan x prove csc 2x frac sec x 2 sin x prove frac sin 3x sin 7x cos 3x cos 7x cot 2x prove frac csc theta cot theta tan theta sin theta cot theta csc theta
Is tan 2x sec 2x 1 an identity Easy Solution Verified by Toppr 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 cos 2xsin 2x cos 2xcos 2x cos 2x1 Sec 2 1 sec 2 sec 2 sec 2 1 sec 2 1 cos 2 sin 2 sec 2 1 sec 2 sec 2 sec 2 1 sec 2 1 cos 2 sin 2 Analysis In the first method we used the identity sec 2 tan 2 1 sec 2 tan 2 1 and continued to simplify
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How is this possible tan 2 is equal to sec 2 according to the calculations they re just ignoring the one at the end of that original argument we re trying to simplify like it wasn t there If sin 2 cos 2 tan 2 1 Sep 7 2015 Using the Pythagorean identity tan2x sec2x 1 Explanation This is an application of the Pythagorean identities namely 1 tan2x sec2x This can be derived from the standard Pythagorean identity by dividing everything by cos2x like so cos2x sin2x 1 cos2x cos2x sin2x cos2x 1 cos2x 1 tan2x sec2x
Ask Question Asked 12 years 10 months ago Modified 8 years 8 months ago Viewed 7k times 3 I need to prove that 1 tan x tan 2x sec 2x 1 tan x tan 2 x sec 2 x I started this by making sec 1 cos and using the double angle identity for that and it didn t work at all in any way ever One of my 9th grade students asked How can we say sec2x tan2x 1 is an identity since when we plug in x 2 the identity fails which creates an ambiguity for the definition of an identity in mathematics How should I try to explain him without entering into calculus part secondary education trigonometry Share Improve this
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is tan 2x sec 2x 1 an identity - Prove tan 2 x sin 2 x tan 2 x sin 2 x prove cot 2x frac 1 tan 2 x 2 tan x prove csc 2x frac sec x 2 sin x prove frac sin 3x sin 7x cos 3x cos 7x cot 2x prove frac csc theta cot theta tan theta sin theta cot theta csc theta