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These are your basic building blocks for solving trigonometric equations and understanding how the pieces fit together. Using these identities can make sense of even the scariest looking trig.

Find the value of

\[\cos^2 45^{\circ} +\sin^2 45^{\circ}.\]

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Simplify \( \tan\left(A + \frac{\pi}{2}\right).\)

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If \(\sin A +\sin^{2}A=1,\) find the value of \(\cos ^{2} A + \cos ^{4} A.\)

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\[\ln(\tan1^{\circ})+ \ln(\tan2^{\circ})+\ldots+\ln(\tan88^{\circ})+\ln(\tan89^{\circ})= \ ?\]

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What is the value of \( \sin 20^{\circ}(\tan 10^{\circ}+\cot 10^{\circ})\)?

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