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#