Answer the following:a) Ifsin-¹|2|<-1T.2Prove|sin¯¹z|< sin¯¹|z|< -b) prove thatในประเทศtan"¹ z =) (-1)" =Z2n +1n=0c) prove that2n-1Zsin ¹z=z+1/²·+=+...+(-1)”3 53+1/12Z3+1.3552n-1auto ...2n+1+...

Given: sin-1z<π2 To prove: a) sin-1z<sin-1z<π2b)…

Answered: Answer the following: a) If…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If, Sec t-1/sec t +1 = A-cos t/A+cos t Then A =
6) Use Linear Property to find ( 1 - 3 x4) ' A) (1– 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use Product Rule to find [(1 – 3 x4)(sin x) ] ' = A) -12 x3 (sin x) + (1 – 3 x4)(cos x) C) -12 x3 (cos x) + (1 – 3 x4)(cos x) 7) B) -12 x3 (sin x) + (1 – 3 x4)(sin x) D) -12 x3 (cos x) + (1 – 3 x4)(sin x) 8) Use Quotient Rule to find [(1 – 3 x4)/(sin x) ] ' =, A) [-12 x3 (cos x) + (1 – 3 x4)(cos x) ]/ sin2 x B) [-12 x3 (sin x) – (1 – 3 x4)(cos x) ]/ sin2 x C) [-12 x3 (cos x) – (1 – 3 x4)(cos x) ]/ cos2 x D) [-12 x³ (sin x) – (1 – 3 x4)(cos x) ]/ cos2 x 8) 9) Use Power Rule to find [(1 – 3 x*)25 ] ' = A) -25(1 - 3 x4)24 x3 C) -300(1 – 3 x*)100 x3 9) B) -12(1 - 3 x9)24 D) -300(1 - 3 x4)24 x3
12. Prove that sin? 0 – sin* 0 = cos? 0 – cos' 0.
Please help it’s one exercise
b) 1+tanx 1–tanx = tan (x + 1)
1 Prove that : sec q + tan q = 2x or, 4x 1 If sec q = x+ 2х
Verify and write the justification
4. Prove that tan² x – cos x = sec² x – cos x - cos“ x = x- cos'x– 1.
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Q/IF 3= sin(x-10-²³ (4) 2 y` = 3² sin(x) cos(x) Prove that
V3 1) tan 3 -1 2) cos -1 3) sin-0 4) tan-1 (-V3) 5) tan -1 6) sin 2 -1 8) tan -1 7) cos 2
Erercise(1) Show that 1 1. sec- x = cos -1 2.글cos-1x = tan-1 1-x 1+x Find the exact value 1.cos[sin-- + tan-1 3 2. tan ( tan 3 -1 sin -1 taan a-tanb [Hint: tan(a – b): 1+tanatanb A.

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Answer the following: a) If sin=-¹|2|<1/1 Prove |sin" =