Show that:
Tan∅+ Cot∅ = Sec∅. Cosec∅
Answers
Answered by
8
LHS = Tan∅
= Sin²∅+Cos²∅/ sin∅cos∅
= 1/sin∅cos∅ ( sin²∅+cos²∅ = 1 ) ( 1/cos∅= Sec∅, 1/sin∅= cosec∅)
= Sec∅.cosec∅
Hence Proved
= Sin²∅+Cos²∅/ sin∅cos∅
= 1/sin∅cos∅ ( sin²∅+cos²∅ = 1 ) ( 1/cos∅= Sec∅, 1/sin∅= cosec∅)
= Sec∅.cosec∅
Hence Proved
Answered by
5
LHS = tan∅ + cot∅
= sin∅/cos∅ + cos∅/sin∅
= { sin²∅ + cos²∅}/sin∅.cos∅
we know,
sin²∅ + cos²∅ = 1 use this here,
= 1/sin∅.cos∅
= cosec∅.sec∅ = RHS
= sin∅/cos∅ + cos∅/sin∅
= { sin²∅ + cos²∅}/sin∅.cos∅
we know,
sin²∅ + cos²∅ = 1 use this here,
= 1/sin∅.cos∅
= cosec∅.sec∅ = RHS
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