Question

if sinA + cosA = v2, find the value of sinAcosA​

Answer 1

Answer:

4d

Explanation:

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