prove that
tan^2 a + cot^2 a = sec^2 a cosec^2 a -2
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Step-by-step explanation:
LHS
LHS
tan² a + cot²a
Keep the LHS as it is.
Try to start with the more complicated side.i.e here RHS.
RHS
sec²a cosec²a - 2
= (1 + tan²a)(1 + cot²a) - 2 [sec²a - tan²a = 1] and [cosec²a - cot²a =1]
= 1(1 + cot²a) + tan²a(1 + cot²a) - 2
= 1 + cot²a + tan²a + (tan²a× cot²a) - 2
= cot²a + tan²a + 1 + 1 - 2 [ tan²a = 1/cot²a ]
= tan²a + cot²a + 2 - 2
= tan²a + cot²a + 0
= tan²a + cot²a
= LHS
HENCE PROVED.
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