Prove that sinA - cosA = (sin A - cos A) (1 + sin A cos A).
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Answer:
ANSWER
sinA+cosA−1
sinA−cosA+1
=
sinA−(1−cosA)
sinA+(1−cosA)
=
2sin
2
A
cos
2
A
−2sin
2
2
A
2sin
2
A
cos
2
A
+2sin
2
2
A
=
cos
2
A
−sin
2
A
cos
2
A
+sin
2
A
=
cot
2
A
+1
cot
2
A
−1
=cot(
4
π
−
2
A
)
=
sin(
4
π
−
2
A
)×sin(
4
π
−
2
A
)
cos(
4
π
−
2
A
)×sin(
4
π
−
2
A
)
=
1−cos(
2
π
−A)
sin(
2
π
−A)
=
1−sinA
cosA
=
secA−tanA
1
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