Cosec theta/1+sec theta + 1+sec theta/cosec theta = 2 cosec cube theta(sec theta -1). Prove
Answers
Data is wrong as LHS ≠ RHS for Cosecθ/(1 + Secθ) + (1 + Secθ)/Cosecθ = 2Cosec³θ(Secθ - 1)
Step-by-step explanation:
Cosecθ/(1 + Secθ) + (1 + Secθ)/Cosecθ = 2Cosec³θ(Secθ - 1)
Let say θ = 30°
Cosecθ = 2
secθ = 2/√3
LHS
= 2/(1 + 2/√3) + ( 1 + 2/√3) /2
= 2√3/(√3 + 2) + (√3 + 2)/2√3
= 2√3(2 - √3) + √3(√3 + 2)/6
= ( 12√3(2 - √3) + 3 + 2√3)/6
= (24√3 - 36 + 3 + 2√3)/6
= (26√3 - 33)/6
= 2
RHS =
2(2)³ (2/√3 - 1)
= 16( 2 - √3 )/√3
= 16√3( 2 - √3 )/3
= 32√3( 2 - √3 )/6
= (64√3 - 96)/6
= 2.47575
LHS ≠ RHS
Hence Data is wrong
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Step-by-step explanation:
Prove (Cosec x)/(1+Secx) + (1+Secx)/Cosecx=2Cosec^3x(Secx-1)