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There are 6 basic trig functions.

sin(x) = 1/csc(x)

cos(x) = 1/sec(x)

tan(x) = sin(x)/cos(x) or 1/cot(x)

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

cot(x) = cos(x)/sin(x) or 1/tan(x)

---- In your problem csc(x)*cot(x) we can simplify csc(x).

csc(x) = 1/sin(x)

Similarly, cot(x) = cos(x)/sin(x).

csc(x)*cot(x) = (1/sin[x])*(cos[x]/sin[x])

= cos(x)/sin2(x) = cos(x) * 1/sin2(x)

Either of the above answers should work.

In general, try converting your trig functions into sine and cosine to make things simpler.

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โˆ™ 2009-04-12 02:45:14
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Q: How do you simplify csc theta cot theta?
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Related questions

How do you simplify csc theta -cot theta cos theta?

For a start, try converting everything to sines and cosines.


How do you simplify csc theta cot theta cos theta?

cosec(q)*cot(q)*cos(q) = 1/sin(q)*cot(q)*cos(q) = cot2(q)


Express csc theta in terms of cot theta theta is in quadrant 3?

It is -sqrt(1 + cot^2 theta)


How do you simplify sin theta times csc theta divided by tan theta?

Since sin(theta) = 1/cosec(theta) the first two terms simply camcel out and you are left with 1 divided by tan(theta), which is cot(theta).


Can you simplify 1-cot x?

csc^2x+cot^2x=1


How do i simplify csc theta divided by sec theta?

By converting cosecants and secants to the equivalent sine and cosine functions. For example, csc theta is the same as 1 / sin thetha.


What is csc theta?

That depends on the value of the angle, theta. csc is short for "cosecans", and is the reciprocal of the sine. That is, csc theta = 1 / sin theta.


How do you simplify cos theta times csc theta divided by tan theta?

'csc' = 1/sin'tan' = sin/cosSo it must follow that(cos) (csc) / (tan) = (cos) (1/sin)/(sin/cos) = (cos) (1/sin) (cos/sin) = (cos/sin)2


Verify that Cos theta cot theta plus sin theta equals csc theta?

It's easiest to show all of the work (explanations/identities), and x represents theta. cosxcotx + sinx = cscx cosx times cosx/sinx + sinx = csc x (Quotient Identity) cosx2 /sinx + sinx = csc x (multiplied) 1-sinx2/sinx + sinx = csc x (Pythagorean Identity) 1/sinx - sinx2/sinx + sinx = csc x (seperate fraction) 1/sinx -sinx + sinx = csc x (canceled) 1/sinx = csc x (cancelled) csc x =csc x (Reciprocal Identity)


What is cos theta multiplied by csc theta?

It is cotangent(theta).


How do you simplify csc theta minus cot x theta times cos theta plus 1?

There can be no significant simplicfication if some of the angles are theta and others are x, so assume that all angles are x. [csc(x) - cot(x)]*[cos(x) + 1] =[1/sin(x) - cos(x)/sin(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos2(x)] =1/sin(x)*[sin2(x)] = sin(x)


What is the derivative of csc x?

The derivative of csc(x) is -cot(x)csc(x).


If tan Theta equals 2 with Theta in Quadrant 3 find cot Theta?

Cotan(theta) is the reciprocal of the tan(theta). So, cot(theta) = 1/2.


How do you simplify sec x cot x?

sec(x)*cot(x) = (1/cos(x))*(cos(x)/sin(x)) = (1/sin(x)) = csc(x)


Tan theta plus cot theta equals 2csc2 theta?

Yes, it is.


How do you get the csc theta given tan theta in quadrant 1?

If tan(theta) = x then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x = sqrt(1 + 1/x2)


What is tan theta minus cot theta?

-2(cot2theta)


What is the anti derivative of cscxcotx?

∫cscxcotx*dx∫csc(u)cot(u)*du= -csc(u)+C, where C is the constant of integrationbecause d/dx(csc(u))=-[csc(u)cot(u)],so d/dx(-csc(u))=csc(u)cot(u).∫cscxcotx*dxLet:u=xdu/dx=1du=dx∫cscucotu*du= -csc(u)+CPlug in x for u.∫cscxcotx*dx= -csc(x)+C


What is cot x sin x simplified?

To simplify such expressions, it helps to express all trigonometric functions in terms of sines and cosines. That is, convert tan, cot, sec or csc to their equivalent in terms of sin and cos.


How do you integrate the cscnx?

The integral for csc(u)dx is -ln|csc(u) + cot(u)| + C.


How can you verify 1 plus tan theta divided by 1 minus tan theta equals cot theta plus 1 divided by cot theta minus 1?

It depends if 1 plus tan theta is divided or multiplied by 1 minus tan theta.


What can the function cotangent theta also be expressed as?

cot theta=tan(90-tetha)


If tansqtheta plus 5tantheta0 find the value of tantheta plus cottheta?

tan2(theta) + 5*tan(theta) = 0 => tan(theta)*[tan(theta) + 5] = 0=> tan(theta) = 0 or tan(theta) = -5If tan(theta) = 0 then tan(theta) + cot(theta) is not defined.If tan(theta) = -5 then tan(theta) + cot(theta) = -5 - 1/5 = -5.2


How do you simplify cot of theta times sin of theta?

By converting everything to sines and cosines. Since tan x = sin x / cos x, in the cotangent, which is the reciprocal of the tangent: cot x = cos x / sin x. You can replace any other variable (like thetha) for the angle.


What is cot theta divided by tan theta plus one equal?

whats the big doubt,cot/tan+1= 1+1= 2