Verify: 4tan(θ)sec(θ) = (1+sin(θ)/1−sin(θ)) − (1−sin(θ)/1+sin(θ))

Working with the right side,

(1 + sin(θ))/(1 - sin(θ)) - (1 - sin(θ))/(1 + sin(θ))

multiply the first term by (1 + sin(θ))/(1 + sin(θ)) and the second one by (1 - sin(θ))/(1 - sin(θ)). This gives

(1 + sin(θ))/(1 - sin(θ)) • (1 + sin(θ))/(1 + sin(θ)) = (1 + sin(θ))^2 / (1 - sin^2(θ))

… = (1 + sin(θ))^2 / cos^2(θ)

and

(1 - sin(θ))/(1 + sin(θ)) • (1 - sin(θ))/(1 - sin(θ)) = (1 - sin(θ))^2 / (1 - sin^2(θ))

… = (1 - sin(θ))^2 / cos^2(θ)

Now combine the fractions, expand the numerator, and simplify:

(1 + sin(θ))^2 / cos^2(θ) - (1 - sin(θ))^2 / cos^2(θ) = ((1 + sin(θ))^2 - (1 - sin(θ))^2) / cos^2(θ)

… = ((1 + 2 sin(θ) + sin^2(θ)) - (1 - 2 sin(θ) + sin^2(θ))) / cos^2(θ)

… = 4 sin(θ) / cos^2(θ)

… = 4 • sin(θ)/cos(θ) • 1/cos(θ)

… = 4 tan(θ) sec(θ)

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if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

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