without making wronskian show that following are linearlydependent cos 2 (x) , s

Question

without making wronskian show that following are linearlydependent cos2 (x) , sin2(x),sec2(x), tan2(x) in theinterval(-pi/2..pi/2)
make linear combination to show thatthey are linearly dependent i am sure they must be linearlydependent because we can write one in terms of other but howwe can prove by linear combination
cos2 (x) , sin2(x),sec2(x), tan2(x) in theinterval(-pi/2..pi/2)
make linear combination to show thatthey are linearly dependent i am sure they must be linearlydependent because we can write one in terms of other but howwe can prove by linear combination

Explanation / Answer

I'll make use of the trigonometric identitiessin2(x)+cos2(x) = 1 and 1+tan2(x)= sec2(x) to show they are linearly dependent by findinga linear combination that sums to 0.sin2(x)+cos2(x)+tan2(x)-sec2(x)= 1 - 1 = 0

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