prove that LHS is equal to RHS
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√(1 + sin∅)/√(1 - sin∅)
= √(1 + sin∅) × √(1 + sin∅)/√(1 -sin∅)×√(1 +sin∅)
= √(1 + sin∅)²/√(1 -sin²∅)
= (1 + sin∅)/√cos²∅
= (1 + sin∅)/cos∅
= 1/cos∅ + sin∅/cos∅
= sec∅ + tan∅
hence lhs=rhs
= √(1 + sin∅) × √(1 + sin∅)/√(1 -sin∅)×√(1 +sin∅)
= √(1 + sin∅)²/√(1 -sin²∅)
= (1 + sin∅)/√cos²∅
= (1 + sin∅)/cos∅
= 1/cos∅ + sin∅/cos∅
= sec∅ + tan∅
hence lhs=rhs
Answered by
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√1+sinA/1-sinA= secA+tanA
LHS,
√(1+sinA)(1+sinA)/(1-sinA) (1+sinA)
=√(1+sinA)²/1-sin²A
=1+sinA/cosA
=1/cosA+sinA/cosA
=secA+tanA
=RHS
proved RHS = LHS
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