If cosecA + cotA = m , Show that m square -1/ m square + 1 = cosA
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Answered by
17
Given : Cosec A + cot A=m
m=1/sinA + cosA/sinA
=(1+cosA)/sinA
m²-1⇒(1+cos²A+2cosA-sin²A)/sin²A
⇒(2Cos²A+2CosA)/Sin²A
⇒m²-1=cosAcos²(A/2)/sin²A
m²+1⇒1+cos²A+2CosA+sin²A/sin²A
⇒2(1+cosA)/sin²A
=4cos²(A/2)/sin²A
(m²-1)/(m²+1)⇒[4cosAcos²(A/2)/sin2A]/[4cos²(A/2)/sin²A] = cosA
hence, proved
m=1/sinA + cosA/sinA
=(1+cosA)/sinA
m²-1⇒(1+cos²A+2cosA-sin²A)/sin²A
⇒(2Cos²A+2CosA)/Sin²A
⇒m²-1=cosAcos²(A/2)/sin²A
m²+1⇒1+cos²A+2CosA+sin²A/sin²A
⇒2(1+cosA)/sin²A
=4cos²(A/2)/sin²A
(m²-1)/(m²+1)⇒[4cosAcos²(A/2)/sin2A]/[4cos²(A/2)/sin²A] = cosA
hence, proved
Answered by
1
Answer:
Answer:
=(cosecA+cotA)^2 -1/(cosecA+cotA)^2 +1
=cosec^2A+cot^2A+2cosecAcotA-1/cosec^2A+cot^2A+2cosecAcotA+1
=1+cot^2A+cot^2A+2cosecAcotA-1/cosec^2A+cosec^2A-1+2cosecAcotA+1
=2cotA(cotA+cosecA)/2cosecA(cosecA+cotA)
=cosA/sinA/1/sinA
=cosA
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