Question

What is the value of 2 sin A cos A ?, if A = 221/2​

Answer 1

Answer:

we know that →

→Cos 2θ=Cos^2θ - sin^2θ

→Cos2θ = 1-sin^θ -sin^2 θ

→Cos 2θ = 1- 2sin^2 θ

→2sin^2 θ = 1- cos 2θ

Therefore:

$Sin ^2 θ = (1-cos 2θ)/2----(1)$

→Let θ = 22 1/2

→Put θ value in (1)

→Sin ^2 221/2= (1- cos 2×221/2)/2

=(1-cos 45)/2

=(1 - 1/root2)/2

=(root2- 1)/(2root2)

Therefore:

Sin 221/2= sqrt[(sqrt2 - 1)/2sqrt2]

Answer 2

Answer:

sinA=p/h, =221/2

p=221

h=2

b=?

b=√p2-h2

b=√221^-2^

=√442-4

=√438.

cosA=b/h, =221/2

b=221

h=2

p=?

p=√b^-h^

p=√221^-2^

=√442-4

=√438.

=438×2=876.