How do you solve $sec^2(theta) - sin^2(theta) - cos^2(theta) - tan^2(theta) = 0$ ?

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Answer 1 · 2016-10-09T20:50:24

Substitute identities and combine like terms to obtain: $0 = 0$

Substitute $1 + tan²(theta)$ for $sec²(theta)$ :

$1 + tan²(theta) - sin²(theta) - cos²(theta) - tan²(theta) = 0$

Combine like terms:

$1 - sin²(theta) - cos²(theta) = 0$

Substitute $1 - cos²(theta)$ for $sin(theta)$ :

$1 - (1 - cos²(theta)) - cos²(theta) = 0$

Distribute the minus sign:

$1 - 1 + cos²(theta) - cos²(theta) = 0$

Combine like terms:

$0 = 0$

How do you solve sec^2(theta) - sin^2(theta) - cos^2(theta) - tan^2(theta) = 0sec^2(theta) - sin^2(theta) - cos^2(theta) - tan^2(theta) = 0?