Question

Cosec theta/1+sec theta + 1+sec theta/cosec theta = 2 cosec cube theta(sec theta -1). Prove

Answer 1

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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Answer 2

Step-by-step explanation:

Prove (Cosec x)/(1+Secx) + (1+Secx)/Cosecx=2Cosec^3x(Secx-1)