prove that sec ^ 2 a . cosec ^ 2 a = tan ^ 2 a + cot ^ 2 a + 2
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From RHS
Tan^2= (sin/cos)^2
Cot^2=(cos/sin)^2
taking LCM
we get sin^2 +cos^2/sin^2cos^2
we get 1/sin^2cos^2
sec^2.cosec^2.
Tan^2= (sin/cos)^2
Cot^2=(cos/sin)^2
taking LCM
we get sin^2 +cos^2/sin^2cos^2
we get 1/sin^2cos^2
sec^2.cosec^2.
arnabbis2014p6srha:
where did the 2 go ???
From LHS:
sec^2 a. cosec^2 a
(1+tan^2 a).(cot^2 a +a)
cot^2 a + 1 + tan^2a.cot^2a + tan^2 a
cot^2 a +1 + (tan^2 a)(1/tan^2 a) + tan^2 a
cot^2 a + 1 + 1+ tan^2 a
tan^2 a + cot^2 a + 2
(1+tan^2 a).(cot^2 a +a)
cot^2 a + 1 + tan^2a.cot^2a + tan^2 a
cot^2 a +1 + (tan^2 a)(1/tan^2 a) + tan^2 a
cot^2 a + 1 + 1+ tan^2 a
tan^2 a + cot^2 a + 2
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