sin x /cot x + cosec x = 2+ sinx / cot x - cosec x
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Answered by
19
Answer:
Step-by-step explanation:
L.H.S:
Sinx / Cotx + Cosecx
= Sinx / (Cosx/Sinx) + (1/Sinx)
= Sinx / [(Cosx + 1) / Sinx]
= Sin²x / 1 + Cosx
= 1 - Cos²x / 1 + Cosx
= (1 + Cosx)(1 -Cosx) / 1 + cosx
= 1 - Cosx.
R.H.S:
2 + Sinx / Cotx - Cosecx
= 2 + Sinx / (Cosx/Sinx) - (1/Sinx)
= 2 + Sinx/[(Cosx - 1)/Sinx]
= 2 + Sin²x / (Cosx - 1)
= 2 + (1 - Cos²x) / (Cosx - 1)
= 2 + (1 + Cosx)(1 - Cosx) / (Cosx - 1)
= 2 + (1 + Cosx) * [ -1 (Cosx - 1) ] / (Cosx - 1)
= 2 + (1 + Cosx) ( -1)
= 2 - 1 - Cosx
= 1 - Cosx
∴ L.H.S = R.H.S
Hence proved.
Answered by
8
Step-by-step explanation:
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