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Question
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
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Solution
`tan^2 theta + sin theta = cos^2 theta`
LHS = `tan^2 theta + sin theta `
= `(sin^2 theta)/(cos^2 theta) + sin theta`
= `(1- cos^2 theta )/( cos^2 theta) + sin theta`
= `sec^2 theta - 1 + sin theta `
Since LHS ≠ RHS, this is not an identity.
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