Given that tanx =5/12. Find the value of 1.cosx 2.sinx 3 cos(90-x) 4.sin(180-x)?

1. To find the value of cosx, we can use the Pythagorean identity: cos^2(x) + sin^2(x) = 1. Since we know that tanx = sinx/cosx = 5/12, we can find sinx by sinx = (5/12)cosx. Substituting this into the Pythagorean identity, we get:

cos^2(x) + (5/12)^2cos^2(x) = 1
cos^2(x) + 25/144cos^2(x) = 1
169/144cos^2(x) = 1
cos^2(x) = 144/169
cosx = ±12/13

Since tanx is positive, cosx must also be positive. Therefore, cosx = 12/13.

2. sinx = (5/12)cosx = (5/12)(12/13) = 5/13

3. cos(90-x) = sinx = 5/13

4. sin(180-x) = sinx = 5/13

Given: tanx = 5/12

1. cosx:
Using the Pythagorean identity: tan^2x + 1 = sec^2x, we have:

(5/12)^2 + 1 = sec^2x
25/144 + 1 = sec^2x
169/144 = sec^2x
13/12 = secx
cosx = 12/13

2. sinx:
Using the identity: sinx = cosx / tanx, we have:

sinx = (12/13) / (5/12)
sinx = 5/5 = 1

3. cos(90-x):
Using the identity: cos(90-x) = sinx, we have:

cos(90-x) = sinx
cos(90-x) = 1

4. sin(180-x):
Using the identity: sin(180-x) = -sinx, we have:

sin(180-x) = -(1)
sin(180-x) = -1