Question

The value of tan^2 30 degree + 4sin^2 45 degree + cos^2 30 degree is​

Answer 1

Question

The value of tan^2 30 degree + 4sin^2 45 degree + cos^2 30 degree is

$\huge \bf\orange{Solution}$

$\sf\mapsto\:\:\:\purple{\Big( \dfrac{1}{\sqrt{3}}\Big)^{2} + 4 \Big(\dfrac{1}{\sqrt{2}}\Big)^{2} + \Big( \dfrac{\sqrt{3}}{2}\Big)^{2} }$

$\sf\mapsto\:\:\:\green{ \dfrac{1}{3} + 4 \times \dfrac{1}{2} + \dfrac{3}{4}}$

$\sf\mapsto\:\:\:\purple{ \dfrac{1}{3} + 2 + \dfrac{3}{4}}$

$\sf\mapsto\:\:\:\green{\dfrac{4+8+9}{12}}$

$\sf\mapsto\:\:\:\purple{ \dfrac{\cancel{21}}{\cancel{12}} }$

$\sf\mapsto\:\:\:\green{ \dfrac{7}{4}}$

$\tt\red{\therefore\:\:The \: value \:of \: tan^{2} 30\degree + 4 sin^{2} 45\degree + cos^{2} 30\degree \ = \ \dfrac{7}{4}}$

Answer 2

Question

The value of tan^2 30 degree + 4sin^2 45 degree + cos^2 30 degree is

\huge \bf\orange{Solution}Solution

\sf\mapsto\:\:\:\purple{\Big( \dfrac{1}{\sqrt{3}}\Big)^{2} + 4 \Big(\dfrac{1}{\sqrt{2}}\Big)^{2} + \Big( \dfrac{\sqrt{3}}{2}\Big)^{2} }↦(31)2+4(21)2+(23)2

\sf\mapsto\:\:\:\green{ \dfrac{1}{3} + 4 \times \dfrac{1}{2} + \dfrac{3}{4}}↦31+4×21+43

\sf\mapsto\:\:\:\purple{ \dfrac{1}{3} + 2 + \dfrac{3}{4}}↦31+2+43

\sf\mapsto\:\:\:\green{\dfrac{4+8+9}{12}}↦124+8+9

\sf\mapsto\:\:\:\purple{ \dfrac{\cancel{21}}{\cancel{12}} }↦1221

\sf\mapsto\:\:\:\green{ \dfrac{7}{4}}↦47

\tt\red{\therefore\:\:The \: value \:of \: tan^{2} 30\degree + 4 sin^{2} 45\degree + cos^{2} 30\degree \ = \ \dfrac{7}{4}}∴Thevalueoftan230°+4sin245°+cos230° = 47