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3 years ago

Prove that: sec⁴B - sec²B = tan⁴B + tan²B.

Mathematics

1 answer:

kumpel [21]3 years ago

3 0

Step-by-step explanation:

sec⁴B - sec²B = sec²B(sec²B - 1)

= (1 + tan²B)(tan²B)

= tan⁴B + tan²B

= Right-hand side (Proven)

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For this case we must solve the following quadratic equation:

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The solution of the equation is given by:

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Where:

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Substituting the values we have:

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$x_ {1} = - 1+ \sqrt {17}\\x_ {2} = - 1- \sqrt {17}$

Answer:

$x_ {1} = - 1+ \sqrt {17}\\x_ {2} = - 1- \sqrt {17}$

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Prove that: sec⁴B - sec²B = tan⁴B + tan²B.​

Prove that: sec⁴B - sec²B = tan⁴B + tan²B.