Evaluate: 2 60° + 2 tan 45° ― 2 30°
2 60°
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Answer:
Step-by-step explanation:
Given : Expression \sin^2 60^\circ+2\tan 45^\circ-\cos^2 30^\circsin
2
60
∘
+2tan45
∘
−cos
2
30
∘
To find : Evaluate the expression ?
Solution :
\sin^2 60^\circ+2\tan 45^\circ-\cos^2 30^\circsin
2
60
∘
+2tan45
∘
−cos
2
30
∘
Using trigonometric values,
\sin 60^\circ=\frac{\sqrt3}{2}sin60
∘
=
2
3
\tan 45^\circ =1tan45
∘
=1
\cos 30^\circ=\frac{\sqrt3}{2}cos30
∘
=
2
3
Substitute the values,
=(\frac{\sqrt3}{2})^2+2(1)-(\frac{\sqrt3}{2})^2=(
2
3
)
2
+2(1)−(
2
3
)
2
=\frac{3}{4}+2-\frac{3}{4}=
4
3
+2−
4
3
=2=2
Therefore, \sin^2 60^\circ+2\tan 45^\circ-\cos^2 30^\circ=2sin
2
60
∘
+2tan45
∘
−cos
2
30
∘
=2 .
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