Question

If 1 + secA = x, then the value of x is

Options:

1) sinAtanA/(1 + cosA)

2) √[sinAtanA/(1 - cosA)]

3) sinAtanA/(1 - cosA)

4) √[sinAtanA/(1 + cosA

Answer 1

Hi ,

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We know the trigonometric identity:

1 ) sec² A - 1 = tan² A

And

2 ) tanA = sinA/cosA

3) secA =1/cosA

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Now ,

It is given that ,

x = 1 + secA

x = Sec A + 1

x=[ ( secA+ 1 )( secA - 1 ) ]/( secA - 1 )

x = ( sec²A - 1 )/ ( 1/cosA - 1 )

x = tan² A / [ ( 1 - cosA )/cosA ]

x = ( sin²A/cos²A )/[ (1 - cosA )/cosA ]

x = ( sin²A/cosA ) / ( 1 - cos A )

x = [ sinA ( sinA/cosA ) ]/( 1 - cosA )

x = sinAtanA /( 1 - cosA )

Option ( 3 ) is correct .

I hope this helps you.

: )