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Short answer 2 * sec^2(theta)
Find the common denominator
The common denominator is (1 - sin(theta) * (1 + sin(theta) )
Multiply each fraction's numerator and denominator by the common denominator
Remove the brackets and cancel the sin(theta) terms in the numerator.
Combine the denominator
2 / (1 - sin^2(theta)) but 1 - sin^2(theta) = cos^2(theta)
2 / (cos^2 (theta) but 1/cos^2(theta) = sec^2(theta)
2 * sec^2 (theta) <<<<< Answer
Find the common denominator
The common denominator is (1 - sin(theta) * (1 + sin(theta) )
Multiply each fraction's numerator and denominator by the common denominator
Remove the brackets and cancel the sin(theta) terms in the numerator.
Combine the denominator
2 / (1 - sin^2(theta)) but 1 - sin^2(theta) = cos^2(theta)
2 / (cos^2 (theta) but 1/cos^2(theta) = sec^2(theta)
2 * sec^2 (theta) <<<<< Answer