math
posted by Kayla .
how do i solve this using trig identities?
2 csc^2x = 3 cot^2x1

math 
Reiny
first change everything to sines and cosines
2/(sin^2 x) = 3(cos^2 x)/(sin^2 x)  1
multiply by sin^2 x
2 = 3 cos^2 x  sin^2 x
but sin^2 x  1  cos^2 x
so
2 = 3 cos^2 x  1 + cos^2 x
3 = 4cos^2 x
cos^2 x = 3/4
cos x = ±√3/2
Do you recognize the 1,√3,2 rightangled triangle? If not your calculuator should give you 30º.
if cos x = +√3/2 then x is in the first our fourth quadrants and
x = 30º or 330º
if cos x = √3/2 then x is in the second and third quadrants and
x = 150º or 210º
(in radians the answers would be
pi/6, 11pi/6, 5pi/6,7pi/6)
Respond to this Question
Similar Questions

Trigonometry
Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; … 
verifying trigonometric identities
How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1  sin a)= cos^2a 2. cos^2b  sin^2b = 2cos^2b  1 3. sin^2a  sin^4a = cos^2a  cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t / csc 
Math  Trig
I'm trying to verify these trigonometric identities. 1. 1 / [sec(x) * tan(x)] = csc(x)  sin(x) 2. csc(x)  sin(x) = cos(x) * cot(x) 3. 1/tan(x) + 1/cot(x) = tan(x) + cot(x) 4. csc(x)/sec(x) = cot(x) 
Trigonometry
Use the trig Identities to find the other 5 trig functions. Problem 7.)Tan(90x)=3/8 8.)Csc x=13/5 9.)Cot x=square root of 3 10.)Sin(90x)=.4563 11.)Sec(x)=4 12.)Cos x=.2351 I need HELP! 
trig 30
For csc^2 A1/cot A csc A, what is the simplest equivalent trig expression? 
math
use the quotient and reciprocal identities to simplify the given expression cot t sin t csc t sin t tan t cot t cot t sec t 
Trig verifying identities
I am having trouble with this problem. sec^2(pi/2x)1= cot ^2x I got : By cofunction identity sec(90 degrees  x) = csc x secx csc1 = cot^2x Then split sec x and csc1 into two fractions and multiplied both numerator and denominators … 
Trig identities
Sin x/[1cos(x)] = csc x + cot x Please Verify the Identity. I have been going in circle with this one... Just a hint would be nice. Thank you. 
trig
verify (csc^41)/cot^2x=2+cot^2x So this is what I have so far on the left side (csc^2x+1)(cscx+1)(cscx1)/cot^2x =(csc^2x+1)(cot^2x)/cot^2x i think I'm doing something wrong. Please help! 
Precal
Cot^2xcsc^2x Please help me simplify using identities! Thank You!