Math, asked by bhagyashri10, 1 year ago

2 cosec 2x + cosecx =secx cot (x/2)​

Answers

Answered by amitnrw
4

Answer:

2Cosec2x + Cosecx  = Secx Cot(x/2)

Step-by-step explanation:

2Cosec2x + Cosecx  = Secx Cot(x/2)

LHS

= 2Cosec2x + Cosecx

= 2/Sin2x + 1/Sinx

= 2/2SinxCosx  + 1/Sinx

= 1/SinxCosx + 1/Sinx

= (1 + Cosx)/(SinxCosx)

= Secx (1/Sinx + Cosx/Sinx)

= Secx ( 1 + Cosx)/Sinx

1 + cosx  = 2Cos²(x/2)

Sinx = 2Sin(x/2)Cos(x/2)

= Secx 2Cos²(x/2) /2Sin(x/2)Cos(x/2)

=  Secx Cos(x/2) /Sin(x/2)

= Secx Cot(x/2)

= RHS

QED

Proved

2Cosec2x + Cosecx  = Secx Cot(x/2)

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