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sin(60◦) = √3 /2 

tan(60◦) = √3

6sin(60◦) + 5tan(60◦) = 3√3 + 5√3 = 8√3 = √64√3 = √192

First substiute sin(theta) = x (This step is not nesecessary but often people find quadratics easier to solve in variables that they usually use). Then due to the fact that the "b" coefficient i...

Let's first recall the definition of tan(x) = sin(x)/cos(x). Hence, y' = d/dx( sin(x)/cos(x) ). Recall quotient rule for differentiation: ( f(x)/g(x) )' = ( f '(x)^2*g(x) - f(x)*g'(x)^2 ) / g(x)^2 and tha...

x²-2x+4= (x-2)(x-2)=0  x=-2 (double root)  

x²+5x+1=0

x_1,2= -5+_ (5²-4(1)(1) )^0.5/2 

x₁=4.8     x₂=-0.2 (t...

We use the quotient rule here which states that if y = f(x)/g(x) then dy/dx = (f'(x)g(x) - g'(x)f(x)) / (g(x)^2). Here f(x) = 4x and g(x) = x^2 + 5, so we have f'(x) = 4 , g'(x) = 2x. This gives us dy/dx ...