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Yeah u need double angle then 'draw a triangle,?' Prove 2\cos^{-1}(x)=\cos^{-1}(3x+1) without double angle?

Only things you can assume are basic definitions and axioms and results that are on the data sheet (like \sin^2x+\cos^2x=1)

Both results need the double angle formula which is similar to what I did so will result in the same length of working.

I mean is lying about your atar really that bad? Especially when people had high hopes for you I think 'morally questionable,' is a bit far.

Fair enough, Good Luck for your future!

How does getting your atar change your mind on your course tho?

Why change your preference?

So did speed-O Sound sonic get into med or not? Now Im interested.

You cant assume \sin^{-1}(x)+\cos^{-1}(x)=\frac{\pi}{2} without proof. Nor can you assume 2\cos^{-1} (x) = \cos^{-1} (3x+1)

Yep thanks. I think thats where the confusion was for OP since the textbook makes it look like P_y.

Is it P \times y or P_y, why can you factor out a P like that?

Its always a good idea to state the domain for x before solving so: -1 \leq x \leq 1 and \frac{-2}{3}\leq x \leq 0. Now take the sin of both sides to obtain: \sin(\sin^{-1} (x) - \cos^{-1} (x))=\sin{(\sin^{-1} (3x+1)) \sin(\sin^{-1} (x))\cos(\cos^{-1} (x)) - \sin(\cos^{-1} (x))\cos(\sin^{-1}...

Let X=(2,1,3) Pick two random point on the line say t=0 and t=1 (can be anything really) So let A=(1,-1,2) and B=(3,-1,-1) Then \overrightarrow{AB}=(2,0,-3) and \overrightarrow{AX}=(1,2,1) The vector projection of v onto u is defined as proj_{u}v=\frac{u\cdot v}{|u|^2}u In our case the u is...

Could you show what Q12 is so we actually know what the variables and constants mean?

cool

Theres a bit of a problem with the question (this is why you don't use MIF lol).The dot product can only be negative if the angle between the two vectors is obtuse. Ignoring this: u\cdot v=|u||v|\cos\theta so -6=\sqrt{10}|b|\cos150 \implies |b|=\frac{12}{\sqrt{30}} (I'm assuming they meant...

Im not good at english so take everything I say with a grain of salt. -The main paradox I feel is the use of language to distort meaning in animal farm. The infamous "All animals are equal but some are more equal than others,' is pretty clearly a paradox (how can you be equal but still have...

The dot product is defined as u\cdot v=|u||v|\cos\theta where theta is the angle between the vectors. So a-15=\sqrt{10}\sqrt{a^2+25}\cos120 Since there's square roots its a good idea to square both sides (a-15)^2=10(a^2+25)\left(\frac{1}{4}\right) At this point its just a quadratic. Which...

https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology#:~:text=Mathematical%20and%20theoretical%20biology%20is,biology%20which%20deals%20with%20the Calculus is actually used to model some systems it's pretty cool.

Yes you can also do IBP on the first integral from the third line: I=\int\sin^{99}(x) \sin(100x) \cos{x}dx+\int\sin^{100}(x)\cos(100x) dx to get I=\frac{1}{100}\sin^{100}(x)\sin(100x)-\int\sin^{100}(x)\cos(100x) dx+\int\sin^{100}(x)\cos(100x) dx Which is the same thing.