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2 tan² 45° + cos²30° - sin²60° |
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Answer» 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!!! |
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