Question

if a=30°,verify that cos2a=cos square a minus sin square a= 2 cos square a minus 1

Answer 1

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Answer 2

$\cos2 A=\cos^2 A-\sin^2 A$, verified.

Step-by-step explanation:

We have,

A = 30°

To verify, $\cos2 A=\cos^2 A-\sin^2 A$

L.H.S. $=\cos2 A$

$=\cos2 (30)$

$=\cos 60$ [ ∵ $\cos 60=\dfrac{1}{2}$]

$=\dfrac{1}{2}$

R.H.S.$=\cos^2 A-\sin^2 A$

$=\cos^2 30-\sin^2 30$

$=(\dfrac{\sqrt{3}}{2})^2 -(\dfrac{1}{2})^2$

$=\dfrac{3}{4}-\dfrac{1}{4}$

$=\dfrac{3-1}{4}$

$=\dfrac{2}{4}$

$=\dfrac{1}{2}$

∴ L.H.S. = R.H.S. = $\dfrac{1}{2}$, verified.

Hence, $\cos2 A=\cos^2 A-\sin^2 A$, verified.