UIVe some trigonometric equations By factoring, the square root llerent trigonom
ID: 3146609 • Letter: U
Question
UIVe some trigonometric equations By factoring, the square root llerent trigonometric functions in an equation. Ex.5.p.697 equations Ex. 12.p. 702 Ex.6,p.698 Ex.7.p.698 Ex.8,p.699, Ex.9.p.700 Ex. 10,p 700 equations are solved using a calculator's Ex. 12.p 702 ometric equations have solutions that cannot be determined by knowing the Somerigonometric functions of special angles Such verse trigonometric function feature. ctions of special an in ing the exact Ex.11.p 701 . 651 CS1: .652 653; REVIEW EXERCISES 5.1 e Exercises 1-13, verify each identity L secr-cos x tan x sin x 2 cos x + sin x tan x sec x 654: 655; 655; 656 sin + cosa . sin e-cos. site-cost 12. COs t 1 - cos f 1-tan x = csc x 1 + cos t 5.2 and 5.3 In Exercises 14-19, use a sum or difference formula to find she sin x =-2 tan t sect in t 1 sint+ 1 1 + sin 15, sin 195 11. tan 12 exact value of each expression ntan+1 + tan t sec cos t 16. ta 34 18. cos 650 cos 5+sin 65 sin S 19. sin S0 cos 50P-cos SO' sin S0 sin x cos x cost = cos x (tan + cot )-sec2 + csc 1+Explanation / Answer
1) 1/cosx - cosx
=(1 - cos2 x) / cos x
=sin2 x / cos x
=sinx * sinx / cosx
=tanx sinx
2) cosx + sinx tanx
=cosx + sinx ( sinx / cosx)
=( cos2 x + sin2 x) /cosx = 1/cosx = secx
3) sin2 x (1+ cot2 x )
= sin2 x + sin2 x * cot2 x
=sin2 x + cos2 x =1
4) (sec x-1)(sec x+1)
= sec2 x - 1 = tan2 x (tan2x + 1 = sec2x)
5) (1-tan x) / sinx
= 1/sinx - tanx / sinx
=cscx - sinx/(cosx * sinx)
=csc x -secx
6) 1/(sinx-1) + 1/(sinx+1)
=(sinx+1 + sinx -1) / (sinx-1) (sinx+1)
=2sinx/ sin2 x -1
= 2sinx/ (-cos2 x) = -2 (sinx/cosx) *( 1/ cosx)
= -2 tanx secx
7) (1+sinx) / cos2 x
=1/ cos2 x + sinx/cos2 x
=sec2 x + tanx secx = tan2 x +1 + tanx secx
8) cosx / (1-sinx)
=cosx (1+sinx) / (1-sinx) (1+sinx)
=cosx (1+sinx) / 1-sin2 x = cosx (1+sinx) / cos2 x
=(1+sinx) / cosx
9) 1 - (sin2 x / 1+ cos x)
= 1+cosx -sin2 x / 1+cosx
=cos2 x + cosx / 1+cosx
= cosx(1+cosx) / 1+cosx
=cosx
10) (tanx +cotx)2
= tan2 x + cot2 x + 2 tanx cotx
=tan2 x + cot2 x + 2 = (tan2 x + 1 )+ (cot2 x + 1 ) = sec2 x + csc2 x
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