You should apply the chain rule
d/dx(x.sin x) = x * d/dx(sin x) + sin x * d/dx(x)
= x * cos x + sin x * 1
= x.cos x + sin x
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y = Sin(x) dy/dx = Cos(x)
2sinxsinx=1 (sinx)(sinx)=1/2 sinx=1/4=o.25 since, roughly, for small x values, sin x = x then x=0.25 Otherwise, to be more accurate, we proceed as follows: sinx=0.25 (as given before) then x=arc sin 0.25=0.2526803
-cos(x)
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.