Math, asked by VarmaGadiraju, 9 months ago

Prove that sinA - cosA = (sin A - cos A) (1 + sin A cos A).

Answers

Answered by attarriaan6226
1

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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