prove that(1-sinA+cos A/sinA+cosA-1)=cosecA+cot A
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Answer:
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Step-by-step explanation:
Answer
LHS=
cosA+sinA−1
cosA−sinA+1
dividing Nr and Dr by sinA we get,
=
sinA
cosA
+
sinA
sinA
−
sinA
1
sinA
cosA
−
sinA
sinA
+
sinA
1
=
cotA+1−cosecA
cotA−1+cosecA
=
cotA+1−cosecA
cotA+cosecA−(cosec
2
A−cot
2
A)
=
cotA+1−cosecA
(cotA+cosecA)(1−cosecA+cotA)
=cotA+cosecA=RHS
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