Question

Establish this identity:
(2asin(θ)cos(θ))² + (acos²(θ) - asin²(θ))² = a²

Answer 1

2asin(θ)cos(θ))² + (acos²(θ) - asin²(θ))² = a²
a^2.sin^2 2θ + a^2. cos^2 2θ = a^2
a^2(sin^2 2θ + cos^2 2θ) = a^2
a^2(1) = a^2
LHS = RHS!
ESTABLISHED!! :D
Understood? :D

Answer 2

Use the identities
sin 2θ = 2.sinθ.coθ
And
cos 2θ = cos²θ - sin²θ
And
sin²θ + cos²θ = 1
Got that? :D

Answer 3

\[\left\{ a \left( 2\sin \theta \cos \theta \right)\right\}^{2}-\left\{ a \left( \cos ^{2}\theta-\sin ^{2 }\theta \right) \right\}^{^{2}}\]
\[=a ^{2}\sin ^{2}2\theta+a ^{2}\cos ^{2}2\theta =a^{2}\left( 1 \right)=a ^{2}\]

Answer 4

Ohhhhhhhhh. Okay. I do got it! :D I forgot the like terms things. Thanks! ^^

Answer 5

yw

Answer 6

:)