Question

Double angle identity. Just 5 questions. Really need help as my teacher has been frustrated with me

Answer 1

Answer:

Mark me brainiiest!!

Step-by-step explanation:

Answer 2

The double angle identities are

$\sin(2x)=2\sin x\cos x$

$\cos(2x)=\cos^2x-\sin^2x$

Then

$2\sin\dfrac\pi6\cos\dfrac\pi6=\sin\left(\dfrac{2\pi}6\right)=\sin\dfrac\pi3$

$\cos^2\dfrac\pi{10}-\sin^2\dfrac\pi{10}=\cos\left(\dfrac{2\pi}{10}\right)=\cos\dfrac\pi5$

The second identity together with the Pythagorean identity, $\sin^2x+\cos^2x=1$, gives us another equivalent expression:

$\cos^2x-\sin^2x=\cos^2x-(1-\cos^2x)=2\cos^2x-1$

so

$2\cos^2(0.5)-1=\cos(2\cdot0.5)=\cos1$