Trignometry prove that

Question

Cot 2x - tan 78 = ( sec x sec 78)/2

Answer 1

tan(78)=4.7046 approx; sec(78)=4.8097 approx, therefore sec(x)sec(78)/2=2.4049/cos(x). This is the right-hand side.

Is cot(2x)-4.7046=2.4049/cos(x)? If this is an identity, any value of x will make it true. Put x=45, cot(2x)=cot(90)=tan(0)=0. cos(45)=√2/2=0.7071 approx. But this would mean -4.7046=2.4049√2=3.4010. So the two sides are different, and this is not an identity. So we need to solve for specific value(s) of x.

Amazingly, the answer is x=4, so now we need to find out why.

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