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Elan Coil [88]
3 years ago
8

Verify the identity sec^2(x)tan^2(x)+sec^2(x)=sec^4(x)

Mathematics
1 answer:
Natalija [7]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tan²x + 1 = sec²x ⇒ tan²x = sec²x - 1

Consider the left side

sec²x × tan²x + sec²x

= sec²x(sec²x - 1) + sec²x ← distribute and simplify

= sec^{4} x - sec²x + sec²x

= sec^{4} x = right side ⇒ verified

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