tan² 30 + tan ² 60 + tan ²45
Answers
Answer:
The required value of the expression is 2.
Step-by-step explanation:
Consider the provided information.
\mathrm{2\tan ^2\left(45^{\circ \:}\right)+\cos ^2\left(30^{\circ \:}\right)-\sin ^2\left(60^{\circ \:}\right)}2tan
2
(45
∘
)+cos
2
(30
∘
)−sin
2
(60
∘
)
Substitute \tan \left(45^{\circ \:}\right)=1, \cos \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{2}, \sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}tan(45
∘
)=1,cos(30
∘
)=
2
3
,sin(60
∘
)=
2
3
in above expression.
\mathrm{2\tan ^2\left(45^{\circ \:}\right)+\cos ^2\left(30^{\circ \:}\right)-\sin ^2\left(60^{\circ \:}\right)}=2\cdot \:1^2+\left(\frac{\sqrt{3}}{2}\right)^2-\left(\frac{\sqrt{3}}{2}\right)^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
Step-by-step explanation:
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