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cos(x+a)=cosxcosa-sinxsina so cosa=5 sina=3 which means tana=3/5 a=0.54 RADIANS R=sqrt(5²+3²). =sqrt(34) so sqrt(34)cos(x+0.54)

sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x  dy/dx = 5cos5x y=3cox      dy/dx = -3sinx y=3tan5x     dy/dx = 15sec²(5x) (remember sec(x) is the reciprocal of cos(...

d/dx (xy) = x dy/dx + y 

d/dx (y^2) = 2y dy/dx [This is from the chain rule]

So, d/dx (2x^2 + xy + y^2 = 14) 

=> 4x + x dy/dx + y + 2y dy/dx = 0

set dy/dx = 0 as stationary ...

When dealing with complex numbers and trigonometric functions, always turn to DeMoivre's Theorem that states [cos(θ)+isin(θ)]ⁿ = [cos(nθ)+isin(nθ)]. If we set n=2, the we see a combina...

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Here we need to make a U sibstitution. So we take (x+3) and make this equal U so we now have the integral of u^1/2   . dx

In order to s...