can anyone help me with this
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Hello !!!
Tan A + Sec A - 1 / Tan A - Sec A + 1 = Cos A/1 - Sin A.
LHS = TanA + SecA - 1 / Tan A - Sec A + 1
=> ( Tan A + Sec A ) - ( Sec²A - Tan²A) / ( TanA - SecA + 1 ) [ Since Sec²A - Tan²A = 1 ]
=> ( Tan A + Sec A ) [ 1 - ( Sec A - Tan A ) ] / ( Tan A - SecA + 1 )
=> ( TanA + Sec A ) ( Tan A - SecA + 1 ) / ( TanA - SecA + 1 )
=> ( TanA + Sec A )
=> ( Sin A / Cos A + 1/Cos A )
=> ( 1 + Sin A ) / Cos A
Rationalizing numerator 1 + SinA
=> ( 1 + Sin A ) / Cos A × ( 1 - SinA ) / ( 1 - SinA )
=> ( 1 - Sin²A ) / Cos A ( 1 - Sin A )
=> ( Cos²A ) / CosA ( 1 - Sin A )
=> CosA × CosA / CosA ( 1 - SinA )
=> CosA / ( 1 - Sin A ) = RHS.
Hence,
TanA + SecA -1 / TanA - SecA + 1 = Cos A / 1 + SinA.
★ HOPE IT WILL HELP YOU ★
Tan A + Sec A - 1 / Tan A - Sec A + 1 = Cos A/1 - Sin A.
LHS = TanA + SecA - 1 / Tan A - Sec A + 1
=> ( Tan A + Sec A ) - ( Sec²A - Tan²A) / ( TanA - SecA + 1 ) [ Since Sec²A - Tan²A = 1 ]
=> ( Tan A + Sec A ) [ 1 - ( Sec A - Tan A ) ] / ( Tan A - SecA + 1 )
=> ( TanA + Sec A ) ( Tan A - SecA + 1 ) / ( TanA - SecA + 1 )
=> ( TanA + Sec A )
=> ( Sin A / Cos A + 1/Cos A )
=> ( 1 + Sin A ) / Cos A
Rationalizing numerator 1 + SinA
=> ( 1 + Sin A ) / Cos A × ( 1 - SinA ) / ( 1 - SinA )
=> ( 1 - Sin²A ) / Cos A ( 1 - Sin A )
=> ( Cos²A ) / CosA ( 1 - Sin A )
=> CosA × CosA / CosA ( 1 - SinA )
=> CosA / ( 1 - Sin A ) = RHS.
Hence,
TanA + SecA -1 / TanA - SecA + 1 = Cos A / 1 + SinA.
★ HOPE IT WILL HELP YOU ★
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