2 cosec 2x + cosecx =secx cot (x/2)
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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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