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Solve for 0=<x<360 : 2((tanx)^2) + ((secx)^2) = 1

First step I would take would make it look less intimidating by converting all components into sin and cos i.e 2(((sinx)/(cosx))^2) + 1/((cosx)^2) = 1 Notice that there is a common denominator of cosx^2 so I...
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Answered by Bryan P. • Maths tutor
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Find the exact solution to: ln(x) + ln(7) = ln(21)

Log rules: log(a) + log(b) = log(ab) so, in this case, we must find x such that 7x = 21 thus x = 3 similarly, log(a) - log(b) = log(a/b) rearranging the original equation we get: ln(x) = ln(21) - ln(7) so x ...
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Answered by Bryan P. • Maths tutor
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Write sqrt(50) in the form Asqrt(50) where A is an integer

Note that sqrt(ab)=sqrt(a)sqrt(b) Thus to have A, an integer, we must find the highest number 'a' that is a square number and is also a factor of 50. So, a=25 and b=2 (ab=25x2=50) and we have: sqrt(50) = sqr...
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Answered by Bryan P. • Maths tutor
6281 Views

Prove the identity: sin^2(x)+cos^2(x) = 1

This is one of the most commonly used A level identities which can be proved using only GCSE maths! Firstly, take an arbitrary right angle triangle with Hypotenuse h, and angle x between h and the adjacent s...
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Answered by Sean O. • Maths tutor
5189 Views

Differentiate the function f(x) = x*sin(x)

This function is the product of the two functions 'x' and 'sin(x)'. Therefore we use the product rule, which says that the differential of a product of two functions is the differential of the first multipli...
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Answered by Dylan B. • Maths tutor
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