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note - i will be using ß in place of theta
LHS -
sec²ß - cos²ß
= (1 +tan²ß) -( 1-sin²ß)
= 1 + tan²ß -1 + sin²ß
= tan²ß + sin²ß = rhs
proved.
formula used
sec²ß - tan²ß = 1
sin²ß + cos²ß = 1
other important identity
cosec²ß - cot²ß = 1
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