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we start  y factoring and solving for each equation:

cos(x) (2cos(x) - 1) = 0 

this means: 

cos(x) = 0 and cos(x) = 1/2

from the first equation we get:   x = 90

and from...

Expanding Rsin(x + a): Rsin(x + a) = Rsin(x)cos(a) + Rcos(x)sin(a) Comparing coefficients of sin(x), cos(x) with first expression leads to: Rsin(a) = 2, Rcos(a) = 5 Dividing these equations gives: tan(a) ...

As we are looking for the horizontal displacement first we look at horizontal motion. We know that the horizontal velocity is 15ms^-1 but we dont know the time so we can't work out the horizontal displace...

d/dx(tan^2(x)) is not a known differential, and therefore requires a substitution to calculate it using simpler known differentials.

Using the identity sin^2(x) + cos^2(x) = 1, the equation can be ...

We have, from the formula book, sin⁡(A±B)=sinAcosB±cosAsinB Using A=B=θ, we have sinθ+θ=sinθcosθ+cosθsinθ Which we can simplify to sin2θ=2sinθcosθ as required. We can t...