MHB Solving for $\theta$: Which Value is a Counterexample?

AI Thread Summary
The discussion centers on identifying a counterexample to the identity sin²θ + cos²θ = tan²θ. Participants explore substituting values for θ, specifically pi/4, 5pi/4, and pi/3, to test the validity of the equation. It is concluded that the equation does not hold true universally, as sin²θ + cos²θ equals 1, while tan²θ does not equal 1 for all values of θ. Therefore, the original statement is not an identity. The key takeaway is that there are specific values of θ that demonstrate this discrepancy.
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Which value for $\theta$ is a counterexample to sin^2$\theta$+cos^2$\theta$=tan^2$\theta$ as an identity?

a) pi/4
b) 5pi/4
c) pi/3
d) It is an identity

So I tried subbing in each value (a, b, c) in as x and then finding the exact value from that but I'm not getting it.
 
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Well, you know that $\sin^2\left({x}\right)+\cos^2\left({x}\right)=1$, so the statement you're given above is not an identity, since it does not hold true that $\tan^2\left({x}\right)=1$ for all values of $x$. :)
What can you deduce when you put the numbers on the right side, $\tan^2\left({x}\right)$? (Tongueout)
 
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