Question

evaluate 2 cos square 45 degree + sin square 30 degree minus cos square 60 degree​

Answer 1

Step-by-step explanation:

(1/✓2)×(1/√2)+1/2×1/2-1/2×1/2

1/2 + 1/4 -1/4

2+1-1/4

2/4

=1/2

Answer 2

$2\cos^2 45+\sin^2 30-\cos^2 60$ $=\dfrac{1}{2}$

Step-by-step explanation:

We have,

$2\cos^2 45+\sin^2 30-\cos^2 60$

To find, $2\cos^2 45+\sin^2 30-\cos^2 60$ = ?

∴ $2\cos^2 45+\sin^2 30-\cos^2 60$

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

Using the trigonometric identity,

$\cos 45=\dfrac{1}{\sqrt{2}}, \sin 30=\dfrac{1}{2}$ and

$\cos 60=\dfrac{\sqrt{3}}{2}$

$=2(\dfrac{1}{2})+\dfrac{1}{4}-\dfrac{3}{4}$

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

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

$=\dfrac{2}{4}$

$=\dfrac{1}{2}$

∴ $2\cos^2 45+\sin^2 30-\cos^2 60$ $=\dfrac{1}{2}$