evaluate sin square 30° *sin square 45° + 4tan square 30°
Answers
Step-by-step explanation:
Valueof
sin
2
30°cos
2
45°+4tan
2
30°
+
2
1
sin
2
90°−2cos
2
90°
+
24cos
2
0°
1
=0
Step-by-step explanation:
\begin{gathered}Value \: of \\sin^{2}30\degree cos^{2} 45\degree +4 tan^{2} 30\degree \\+\frac{1}{2} sin^{2} 90\degree -2 cos^{2} 90\degree\\ +\frac{1}{24 cos^{2} 0\degree} \end{gathered}
Valueof
sin
2
30°cos
2
45°+4tan
2
30°
+
2
1
sin
2
90°−2cos
2
90°
+
24cos
2
0°
1
\begin{gathered}=\big(\frac{1}{2}\big)^{2} \times \big(\frac{1}{\sqrt{2}}\big)^{2}+4 \big(\frac{1}{\sqrt{3}}\big)^{2}\\+\frac{1}{2}\times 1-2 \times 0\\+\frac{1}{24\times 1^{2}}\end{gathered}
=(
2
1
)
2
×(
2
1
)
2
+4(
3
1
)
2
+
2
1
×1−2×0
+
24×1
2
1
=\frac{1}{4}\times \frac{1}{2}+4\times \frac{1}{3}+\frac{1}{2}-0+\frac{1}{24}=
4
1
×
2
1
+4×
3
1
+
2
1
−0+
24
1
= \frac{1}{8}+\frac{4}{3}+\frac{1}{2}+\frac{1}{24}=
8
1
+
3
4
+
2
1
+
24
1
=\frac{3+32+12+1}{24}=
24
3+32+12+1
=\frac{48}{24}=
24
48
=2=2
Therefore,
\begin{gathered}Value \: of \\sin^{2}30\degree cos^{2} 45\degree +4 tan^{2} 30\degree \\+\frac{1}{2} sin^{2} 90\degree -2 cos^{2} 90\degree\\ +\frac{1}{24 cos^{2} 0\degree}=2 \end{gathered}
Valueof
sin
2
30°cos
2
45°+4tan
230°+ 21 sin 290°−2cos 2 90°+ 24cos 20⁰1 =2