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Question
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Solution
LHS = sec2A + sec2B
= `1/(cos^2A) + 1/(cos^2 B)`
= `1/(cos^2A) + 1/(cos^2(90° - A))`
= `1/(cos^2 A) + 1/(sin^2 A)`
= `1/( sin^ A. cos^2 A)`
= sec2 A cosec2 A
= sec2 A cosec2 (90° - B)
= sec2A. sec2 B = RHS
Hence proved.
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