math
posted by David .
If 1/cos  cos=a^3 and 1/sin  sin=b^3
Show that tan=a/b

a^3=1/coscos = (1cos^2)/cos=sin^2/cos
b^3=1/sinsin = (1sin^2)/sin=cos^2/sin
a^3/b^3=sin^2/cos * cos^2/sin=sin^3/cos^3
=>
a/b=sin/cos = tan
(Hope you understand your own notations.)
Respond to this Question
Similar Questions

trig
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75  cos145*sin75 (ii) cos35*cos15  sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b)  sin(a)sin)(b) (1)The quantity … 
tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by b and using that cos(b)= cos(b) sin(b)= sin(b) gives: sin(ab) = sin(a)cos(b)  cos(a)sin(b) … 
Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v  u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos … 
algebra
Can someone please help me do this problem? 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1  (3/4)sin^2 2x work on one side only! Responses Trig please help!  Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 … 
Trigonometry
Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees … 
precalculus
For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1tan(x)) c. (cos(x+y))/(cos(xy))= (1tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) … 
Trigonometry desperate help, clueless girl here
2. solve cos 2x3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) 1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that tan(x) … 
MathTrigonometry
Show that if x, y, and z are consecutive terms of an arithmetic sequence, and tan y is defined, then (sin x + sin y + sin z) / (cos x + cos y + cos z) = tan y. So I tried letting x = yk (since x,y,z are consecutive terms of an arithmetic …