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When proving such relations we have a choice, that is we can either start from the left hand side (LHS) and show that it equals the right hand side (RHS) or vice versa. 

I will start with the RHS,

RHS = tan^2(x/2),

          = {sin^2(x/2)} / {cos^2(x/2)},

          = {(1/2)(1+cos(x))} / {(1/2)(1-cos(x))}

          = {1+cos(x)} / {1-cos(x)},

          = {1+(1/sec(x))} / {1-(1/sec(x))},

          = (sec(x)+1) / (sec(x)-1),

          = LHS.

Write this down on a piece of paper, and try to verify each step for yourself.


Maths

Can I please have some help with the following question: Prove that:(sec (x) - 1)/(1 + sec (x)) = (tan^2 (x/2))Thanks 😀

The average radius of our galaxy, The Milky Way, is about 50,000 light years. 

To put that in perspective, if a commercial airliner, let’s say a Boeing 747 flew at a speed of 600mph then it would take approximately 50 billion years to fly from the centre to the edge. So to get from one end to the other, it would take 100 billion years in the plane. 

Our universe is only 14 billion years young...

Raafay Karim

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St Benedict’s Catholic Sixth Form

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Raafay Karim