Question

Simplify the following expression.

sec^2(x) + sin^2(x) - tan^2(x) + cos^2(x)



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Answer 1

Remember the Pythagorean identities:
\(\sin^2 \theta + \cos^2 \theta = 1\)
\(\tan^2 \theta + 1 = \sec^2 \theta \iff \sec^2 \theta - \tan^2 \theta = 1\)
Now look at what you have:
\(\color{red}{sec^2 x} + \color{blue}{\sin^2 x} - \color{red}{\tan^2 x} + \color{blue}{\cos^2 x}\)
Group by color and compare to the identities above.