26, prove that: (tanA+cosecB)-(cotB-secA)-2tanAcotB(cosecA+ secB)27. T

1.	26, prove that: (tanA+cosecB)-(cotB-secA)-2tanAcotB(cosecA+ secB)27. The angle of elevation of the top of a vertical tower from a point on the gr60 degree, from another point 10m vertically above the first, its angle of elevat30 degree. find the height of the tower/
Answer» LHS= (tanA + cosecB)^2 - (cotB-secA)^2= (tan^2A + 2tanAcosecB + cosec^2B) - (cot^2B - 2cotBsecA + sec^2A)= tan^2A + cosec^2B + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA Substituting (tan^2A = sec^2A - 1) and (cosec^2B = 1 + cot^2B) in the above step:(sec^2A - 1) + (1 + cot^2B) + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA= 2tanAcosecB + 2cotBsecA= 2(tanAcosecB + cotBsecA) RHS= 2tanAcotB(cosecA + secB)= 2tanAcotB((1 / sinA) + (1 / cosB))= 2(tanA / sinA)cotB + 2tanA(cot B / cosB)= 2(sinA / (cosAsinB))cotB + 2tanA(cosB / (sinBcosB))= 2(1 / cosA)cotB + 2 tanA(1 / sinB)= 2secAcotB + 2tanAcosecB= 2(secAcotB + tanAcosecB) LHS = RHS

26, prove that: (tanA+cosecB)-(cotB-secA)-2tanAcotB(cosecA+ secB)27. The angle of elevation of the top of a vertical tower from a point on the gr60 degree, from another point 10m vertically above the first, its angle of elevat30 degree. find the height of the tower/

Answer»

LHS= (tanA + cosecB)^2 - (cotB-secA)^2= (tan^2A + 2tanAcosecB + cosec^2B) - (cot^2B - 2cotBsecA + sec^2A)= tan^2A + cosec^2B + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA

Substituting (tan^2A = sec^2A - 1) and (cosec^2B = 1 + cot^2B) in the above step:(sec^2A - 1) + (1 + cot^2B) + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA= 2tanAcosecB + 2cotBsecA= 2(tanAcosecB + cotBsecA)

RHS= 2tanAcotB(cosecA + secB)= 2tanAcotB((1 / sinA) + (1 / cosB))= 2(tanA / sinA)cotB + 2tanA(cot B / cosB)= 2(sinA / (cosAsinB))cotB + 2tanA(cosB / (sinBcosB))= 2(1 / cosA)cotB + 2 tanA(1 / sinB)= 2secAcotB + 2tanAcosecB= 2(secAcotB + tanAcosecB)

LHS = RHS

Discussion

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