verify the following trigonometric identities. cos y 1-sın y 5, sec y + tany= cos x-sin...
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx + tany Which of the following statements verifies that the equation is an identity? O A A tan x-tany tanx+ tany sin?(x - y) V1- cos? (x-y) 11 - cos? (x + y) sin(x - y) sin (x+y) O B. sin (x-y) sin cosy - cos x siny sin x- cos y tan x-tany sin (x+y) sin x cos y + cos x siny sin...
show work 9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x + y) if cosx = - cosy = -— x is in quadrant II and y is in quadrant III. [10] 12. Find the exact value of sin 2x and cos 2x if sin x = and cos x = - [6] 5 13. Simplify tan (x + 3) to a form involving sinx, cosx, and/or tanx. [6]
2. Solve the given trigonometric equation using Pythagorian Identities, cos? 0 + sin? 0 = 1, 1+tan? 0 = sec, cot? 0+1 = csc 0. (a) 1 - 2 sin’x = cos r. (b) 4 sin’t - 5 sin x - 2 cos” x = 2. (c) 2 tang - 2 sec1+1= = tan”.
O TRIGONOMETRIC IDENTITIES AND EQUATIONS Double-angle identities: Problem type 1 3 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in quadrant III. 10 . 0/0 sin 2x = X5 ? cos 2x tan 2x L
Use sum and difference identities to verify which of the following are identities. 1) sin(Q+8) - 1-tan & tan 8 sin a 2-cot a cot 8 2) cos(a+8) - 2 sin a sin 8 Both the equations are identities. None of the equations are identities Only the first equation is an identity. Only the second equation is an identity.
is it A B C D Verify that the trigonometric equation is an identity 1 - CSCX 1+ CSC X = 4 tanx CCX 1+ CSCX 1 - CSGX A. 1 - CSC X 1 + CSC X 1 + cScx 1 - cScx COSX 1)2 - (cos x + 1)2 ( cos x + 1)( cos x + 1) 4 cos x 4 cos x = 4 tan ?xcscx cos2x-1 sin ? B. 1- CSCX 1 + CSCX 1...
2. Prove the identities: (9 marks) b) sin β +tan β 1+sec β sin Cosx- sin x = 1-tanx c) = cos2x+sinxcosx
verify the following 1) tan x+cot y= sin(x+y)/cos x sin y 2) tan 5x + cot 5x = 2 csc 10x
need help with #8, 10 and 11 please! 8. cos x tan x-3cos x=0 Use Identities to Solve Trigonometric Equations Solve on the interval [0,2x). (compare to #7) 9. 2 sin'x-5 cos x+S=0 211-cos? (x) - Scos(x)+s=0 - 2 cos? (x) - 5 cos(x) + 750 2 cos (X)(-cosx+1)+7 (-cosx+1)=0 COSXFO 2 cosx+7=0 X=0 10. sin 2x = cos X 11. sin x = COS X
cos θ cos φ sin φ sin θ, (Beats) Using the trigonometric identities cos(θ verify that φ) (β a) 2 (19) cos ot - cos Bt 2 sin A spring-mass system has an attached mass of 4 g, a spring constant of 16 g/s* and a negligible friction. It is subject to a force of 4 cos(2.2t) down- ward, and is initially 0 at rest. Determine the subsequent motion. Using (19) from Exercise 11, rewrite the solution as the product...