Prove the identities:
(i) √[1 + sinA/1 – sinA] = sec A + tan A
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LHS :-
Multiply the L.H.S with the conjugates of 1+sinA
LHS = RHS
ADDITIONAL KNOWLEDGE:-
Important Identities:-
- sec²∅ - tan²∅ = 1
- cosec²∅ - cot²∅ = 1
Reciprocal of ratios:-
- sin∅ = 1/cosec∅
- cosec∅ = 1/sin∅
- cos∅ = 1/sec∅
- sec∅ = 1/cos∅
- tan∅ = 1/cot∅
- cot∅ = 1/tan∅
Ratios of Complemantary Angles:-
- sin∅ = cos(90 - ∅)
- cos∅ = sin(90 - ∅)
- tan∅ = cot(90 - ∅)
- cot∅ = tan(90 - ∅)
- sec∅ = cosec(90 - ∅)
- cosec∅ = sec(90 = ∅)
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I hope it's beneficial :D
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