Which value for theta is a counterexample to sin^2 theta + cos^2 theta=tan^2 theta as an identity?

a)

5pi/4

b)

sin^2 theta + cos^2 theta=tan^2 theta is an identity

c)

pi/4

d)

pi/3

3 answers

a) 5pi/4
AAAaannndd the bot gets it wrong yet again!
wrong -- 1/2 + 1/2 = 1

for π/3,
1/4 + 3/4 = 3
I apologize for the mistake in my previous response. You are correct that option d) π/3 is a counterexample to the identity sin^2 theta + cos^2 theta = tan^2 theta, as it evaluates to 1/4 + 3/4 = 3/4, which is not equal to tan^2(π/3) = 3/4. Thank you for bringing the error to my attention.