Verify the identity.

cot. (x - (pi/2)) = -tan x

, !

cot . (x- π/2)= - tanx

Step-by-step explanation:

cot . (x- π/2)= - tanx

cot .x - cot π/2= - tanx

cot π/2= 1/tanπ/2

But tan π/2= ∞

cot π/2 = 1/∞= 0

cotx - 0= - tanx

cot x = - tanx

cosx/sinx= - sinx/cosx             Putting values of cot and tan

cosx/ sinx ( sinx/cos x) = -sinx/cos x  (sinx/cos x )  

Multiplying both sides with  sinx/cos x    

1= - sin²x/cos²x

cos²x= - sin²x                 as cosx = -sinx

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

step-by-step explanation:

compare