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a) tan(A+B)=(tanA+tanB)/(1-tanAtanB) So, tan(2x)=[tan(x)+tan(x)]/[1-(tanx)(tanx)]. Therefore, tan(2x)=[2tan(x)]/[1-tan^2(x)] = 2p/(1-p^2). b) cos(x)=1/sec(x). Using other trigonometric identities, we know...

These are two really useful rules for differentiating functions. We use the chain rule when differentiating a 'function of a function', like f(g(x)) in general. We use the product rule when differentiatin...

For the 1st part of the question: use the double angle formula to rewrite cos(2x) = cos^2(x) - sin^2(x). Then use the basic identity to write cos^2(x) = 1-sin^2(x), hence cos(2x) = 1-2sin^2(x). Plug the r...

I like to address this question by using similar fractions. That is to say x/y=2x/2y X over y is the same as 2x over 2y In this example we are asked what the full price of the dress is, as in what 100% of...

General rule for any right angled triangle: a^2+b^2=c^2, with a and b being the shorter sides and c being the hypotenuse (the longest side). Using the equation: a=7 and b = 11 and c=hypotenuse we want to ...