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This question is a quadratic equation in hiding. The first step to solving this would be to expand sec^(2)(x) into 1 + tan^(2)(x) as they are equivalent. This can be derived by dividing sin^(2)(x) + cos^(...

We will solve the integral by part. We know the formula for integration by parts: ∫ f(x)'g(x)dx=f(x)g(x)-∫f(x)g(x)'dx (1). We know that: (arcsin (x))'=1/sqrt(1-x^2). So w...

Problems like this usually look something like: Find the differential of (x² e^2x). The product rule is used when we have to differentiate two different functions multiplied by eachot...

The key word in the question is 'shortest'. The shortest distance from a point to a line is always the perpendicular distance. If we calculate the appropriate angles and lengths/distances, we can use trig...

This question can be treated like a normal binomial expansion question which is commonly seen at A level. The standard binomial expansion is (1+x)ⁿ = 1 + nx + (n(n-1)(x²))/2! where 2...