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Question

Prove that
sec(270A)sec(90A)tan(270A)tan(90+A)+1=0.

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Solution

sec(270A)sec(90A)tan(270A)tan(90+A)+1

=(cosecA)(cosecA)(cotA)(cotA)+1

=cot2Acosec2A+1

=1+1 (Since, cosec2Acot2A=1)

=0

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