Question

prove tha Sin 2x(tanx+cotx)=2

Answer 1

here is your answer

L.H.S.
Sin2x (tanx+cotx)

2sinxcos x ( sinx/cosx + cosx/sinx) { Sin2A = 2sinx cos x}
{ tanx= sinx/cosx , cot = cosx/sinx}

2sinx cosx ( sin^2x + cos^2x/ cosx sinx)

{sin & cos are cancel }

2 × (sin^2x + cos^2x) { sin^2x+ cos^2x =1}

2 ×1

2
L.H.S.=R.H.S

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