== cot(x)== 1/tan(x) = cos(x)/sin(x)
Now substitute cos(x)/sin(x) into the expression, in place of cot(x)
So now:
sin(x) cot(x) cos(x) = sin(x) cos(x) (cos(x)/sin(x) )
sin(x) cos(x) cos(x)/sin(x)
The two sin(x) cancel, leaving you with cos(x) cos(x)
Which is the same as cos2(x)
So:
sin(x) cot(x) cos(x) = cos2(x) ===
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to simplify Cosx=Sinx Tanx you should remember your fundamental and pythagorean identities.. Cosx + Sinx Tanx Cosx + Sinx (Sinx/Cosx) <---------- From Tanx= Sinx/Cosx Cosx + Sin2x/ Cos x <------------- do the LCD Cosx (Cosx/Cosx) + Sin2x/Cosx (Cos2x+Sin2x)/Cosx 1/Cosx <--------- From Sin2x + Cos2x =1 or Secx <-------- answer Comment if you have questions...:))
cosx + sinx = 0 when sinx = -cosx. By dividing both sides by cosx you get: sinx/cosx = -1 tanx = -1 The values where tanx = -1 are 3pi/4, 7pi/4, etc. Those are equivalent to 135 degrees, 315 degrees, etc.
No; sin2x = 2 cosx sinx
2sinxcosx-cosx=0 Factored : cosx(2sinx-1)=0 2 solutions: cosx=0 or sinx=.5 For cosx=0, x=90 or 270 degrees For sinx=.5, x=30 degrees x = {30, 90, 270}
take out the constant -2 then take the intergral of cosx this will give you sinx your answer is -2sinx