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Question
If A and B are complementary angles, prove that:
cosec2 A + cosec2 B = cosec2 A cosec2 B
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Solution
Since, A and B are complementary angles, A + B = 90°
cosec2 A + cosec2 B
= cosec2 A + cosec2 (90° – A)
= cosec2 A + sec2 A
= `1/sin^2A+1/cos^2A`
= `(cos^2A + sin^2A)/(sin^2Acos^2A)`
= `1/(sin^2Acos^2A)`
= cosec2 A sec2 A
= cosec2 A sec2 (90° – B)
= cosec2 A cosec2 B
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