How do you use the fundamental identities to prove other identities?

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How do you use the fundamental identities to prove other identities?

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Answer 1 · 2015-02-22T17:19:19

Divide the fundamental identity ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x + cos^2x = 1$ by ${sin}^{2} x$ $sin^2x$ or ${cos}^{2} x$ $cos^2x$ to derive the other two:

$\frac{{sin}^{2} x}{{sin}^{2} x} + \frac{{cos}^{2} x}{{sin}^{2} x} = \frac{1}{{sin}^{2} x}$ $sin^2x/sin^2x + cos^2x/sin^2x = 1/sin^2x$

$1 + {cot}^{2} x = {csc}^{2} x$ $1 + cot^2x = csc^2x$

$\frac{{sin}^{2} x}{{cos}^{2} x} + \frac{{cos}^{2} x}{{cos}^{2} x} = \frac{1}{{cos}^{2} x}$ $sin^2x/cos^2x + cos^2x/cos^2x = 1/cos^2x$

${tan}^{2} x + 1 = {sec}^{2} x$ $tan^2x + 1 = sec^2x$

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How do you use the fundamental identities to prove other identities?

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