SinA+cosA/sinA-cosA + sinA-cosA/sinA+cosA =2sec²A /tan²-1
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Answered by
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Hii friend,
SinA+CosA/SinA-CosA + SinA-CosA/SinA+CosA. = 2Sec²A/Tan²-1
LHS=> SinA+CosA/SinA-CosA + SinA-CosA/SinA+CosA
=> (SinA+CosA)² + (SinA-CosA)²/(SinA-CosA)(SinA+CosA)
=> 2(Sin²A+Cos²A)/(SinA-Cos²A)
=> 2/(Sin²A-Cos²A)
=> 2/Cos²A
____________
=> (Sin²A/ Cos²A -1) [ On dividing num and denominator by Cos²A]
=> 2Sec²/ Tan²-1 [ 1/Cos = Sec and SinA/Cos A = TanA]
=> 2Sec²A/Tan²-1 = RHS
Therefore,
LHS = RHS
HOPE IT WILL HELP YOU....... :-)
SinA+CosA/SinA-CosA + SinA-CosA/SinA+CosA. = 2Sec²A/Tan²-1
LHS=> SinA+CosA/SinA-CosA + SinA-CosA/SinA+CosA
=> (SinA+CosA)² + (SinA-CosA)²/(SinA-CosA)(SinA+CosA)
=> 2(Sin²A+Cos²A)/(SinA-Cos²A)
=> 2/(Sin²A-Cos²A)
=> 2/Cos²A
____________
=> (Sin²A/ Cos²A -1) [ On dividing num and denominator by Cos²A]
=> 2Sec²/ Tan²-1 [ 1/Cos = Sec and SinA/Cos A = TanA]
=> 2Sec²A/Tan²-1 = RHS
Therefore,
LHS = RHS
HOPE IT WILL HELP YOU....... :-)
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3
Hopefully this will help you.
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