2 tan² 45° + cos²30° - sin²60°
Answers
Step-by-step explanation:
The required value of the expression is 2.
Step-by-step explanation:
Consider the provided information.
\mathrm{2\tan ^2(45^{\circ \:})+\cos ^2(30^{\circ \:})-\sin ^2(60^{\circ \:})}2tan
2
(45
∘
)+cos
2
(30
∘
)−sin
2
(60
∘
)
Substitute \tan (45^{\circ \:})=1, \cos (30^{\circ \:})=\frac{\sqrt{3}}{2}, \sin (60^{\circ \:})=\frac{\sqrt{3}}{2}tan(45
∘
)=1,cos(30
∘
)=
2
3
,sin(60
∘
)=
2
3
in above expression.
\mathrm{2\tan ^2(45^{\circ \:})+\cos ^2(30^{\circ \:})-\sin ^2(60^{\circ \:})}=2\cdot \:1^2+(\frac{\sqrt{3}}{2})^2-(\frac{\sqrt{3}}{2})^22tan
2
(45
∘
)+cos
2
(30
∘
)−sin
2
(60
∘
)=2⋅1
2
+(
2
3
)
2
−(
2
3
)
2
=2+\frac{3}{4}-\frac{3}{4}=2+
4
3
−
4
3
=2=2
Hence, the required value of the expression is 2.
Hope it's Helpful!!!
Step-by-step explanation:
