Question

Sin theta = 24/25, cos theta > 0, Find cos(2theta)

Answer 1

Hello : 
co(x+x) cos(x)cos(x) -sin(x)sin(x)= cos²(x)  -sin²(x)
 = (1-sin²(x)) -sin²(x)
cos(2x) = 1-2sin²(x)
in this exercice : x = θ     sin(θ) = 24/25 and cos(θ) > 0
cos(2θ) = 1 -2(24/25)²....calculate

Answer 2

Well... you don't necessarily need to get the cosine value, in order to get the double angle

$\bf \textit{Double Angle Identities} \\ \quad \\ sin(2\theta)=2sin(\theta)cos(\theta) \\ \quad \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ \boxed{1-2sin^2(\theta)}\\ 2cos^2(\theta)-1 \end{cases} \\ \quad \\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\ -------------------------------\\\\ cos(2\theta )=1-2sin^2(\theta )\qquad \qquad sin(\theta )=\cfrac{24}{25} \\\\\\ cos(2\theta )=1-2\left( \cfrac{24}{25} \right)^2\implies cos(2\theta )=-0.8432$