Question

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SinA + CosA = 2
SinA - CosA = ?​

Answer 1

Answer:

ANSWER

sinA+cosA=

2

(given)

Squaring both sides, we have

(sinA+cosA)

2

=(

2

)

2

sin

2

A+cos

2

A+2sinAcosA=2

(1−cos

2

A)+(1−sin

2

A)+2sinAcosA=2(Using identity:sin

2

θ+cos

2

θ=1)

1−cos

2

A+1−sin

2

A+2sinAcosA=2

⇒2−(cos

2

A+sin

2

A−2sinAcosA)=2

⇒2−(sinA−cosA)

2

=2

⇒(sinA−cosA)

2

=2−2

⇒(sinA−cosA)

2

=0

⇒sinA−cosA=0

Answer 2

$\huge\bf{Answer}$

$\sf(sinA + cosA)=2 \\\sf Squaring \: \: on \: both \: sides ,we \: have\\ \sf (sinA + cosA) ^{2} = 2 ^{2} \\ \sf sin ^{2}A + cos ^{2} A + 2sinAcosA = 4 \\\sf 1 - cos ^{2}A +1 - sin ^{2} A + 2sinAcosA = 4 \\\sf 2 - (cos^{2}A + sin ^{2} A - 2sinAcosA) = 4 \\ \sf(cosA - sin A) ^{2} = 4 - 2 \\ \sf(cos A - sin A) ^{2} = 2 \\ \sf(cos A - sin A) = \sqrt{ 2 } \\ \\ \boxed{\therefore \sf(cos A - sin A) = \sqrt{ 2 }}$