Geometry
# Fundamental Trigonometric Identities

Find the value of

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

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

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

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

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

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