sec x 1 sqrt 2 1 tan x Solution Verified by Toppr secx 1 2 1 tanx 1 cosx 1 tan 8tanx 1 cosx cosx sinxsin 8 cosxcos 8 cos 8 cosxcos 8 sinxsin 8 sinxsin 8 cosxcos 8
3 Solve secx 1 2 1 tanx Case 1 Square both the sides and using sec2x 1 tan2x And solving the quadratic we get answer tanx 1 or tanx 0 Putting them back in also solves the equation Thus x is either n or x n 4 n Z Case 2 secx 1 2 1 tanx 1 cosx cosx 2 1 sinx cosx 2sin2x 2 2 1 2sinx Using the Pythagorean Identity sec2 x tan2 x 1 this can be rewritten as tan2 y 1 x Manipulating the equality yields tan y x2 1 y tan 1 x2 1 which means sec 1 x tan 1 x2 1 Share Cite edited Feb 8 2019 at 16 06 answered Feb 8 2019 at 14 40 KM101 7 176 1 10 26
sec x 1 sqrt 2 1 tan x
sec x 1 sqrt 2 1 tan x
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Free math problem solver answers your trigonometry homework questions with step by step explanations 2 Answers Guillaume L Aug 2 2018 tan sec 1 x x2 1 Explanation tan sec 1 x tan cos 1 1 x let y cos 1 1 x x 1 cos y x2 1 cos y 2 x2 1 1 cos y 2
X tan y x sin y cos y x2 sin y 2 cos y 2 x2 1 cos y 2 sin y 2 1 cos y 2 x2 1 sec y 2 x2 1 sec y sec tan 1 x 0 Here s our answer Answer link sec tan 1 x sqrt x 2 1 sec tan 1 x let y tan 1 x x tan y x sin y cos y x 2 sin y 2 cos y 2 x 2 1 cancel cos y 2 sin y 2 1 You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine The following particularly the first of the three below are called Pythagorean identities sin 2 t cos 2 t 1 tan 2 t 1 sec 2 t 1 cot 2 t csc 2 t Advertisement
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I understand it can be very easily solved by expanding in terms of sinx and cosx gives x 2n 4 But what if I do the following 2secx tanx 1Differentiating 2secxtanx sec2x 0 2tanx secx 0 Step 1 secx 2tanx 1 tanx 2 2tanx tanx 1 tanx 1x n 4 Step 2 tanx 1 2secx Sqrt 1 tan 2 x abs sec x Using cos 2 x sin 2 x 1 tan x sin x cos x sec x 1 cos x we find sqrt 1 tan 2 x sqrt 1 sin 2 x cos 2 x color white sqrt 1 tan 2 x sqrt cos 2 x cos 2 x sin 2 x cos 2 x color white sqrt 1 tan 2 x sqrt cos 2 x sin 2 x cos 2 x color white sqrt 1 tan 2 x
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sec x 1 sqrt 2 1 tan x - You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine The following particularly the first of the three below are called Pythagorean identities sin 2 t cos 2 t 1 tan 2 t 1 sec 2 t 1 cot 2 t csc 2 t Advertisement