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1 mark

If (secA−tanA)
2
=x, then the value of x is:

  1. A
    1−sinA
    1+sinA
  2. B
    1+sinA
    1−sinA



  3. C
    1+sinA
    1−sinA
  4. D
    1−sinA
    1+sinA



Solution & Step-by-step Explanation

Let's simplify the expression (secA−tanA)
2
:

x=(
cosA
1


cosA
sinA

)
2

x=(
cosA
1−sinA

)
2

x=
cos
2
A
(1−sinA)
2



Using the identity cos
2
A=1−sin
2
A:

x=
1−sin
2
A
(1−sinA)
2



x=
(1−sinA)(1+sinA)
(1−sinA)(1−sinA)


x=
1+sinA
1−sinA

Practice this question

Try it yourself before checking the explanation above.

If (secA−tanA)
2
=x, then the value of x is:
A
1−sinA
1+sinA
B
1+sinA
1−sinA



C
1+sinA
1−sinA
D
1−sinA
1+sinA



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