Find the value of sin^2 30 degree + cos^2 30 degree + tan^2 45 degree.
I will mark the best answer as BRAINLIEST.
Answers
Step-by-step explanation:
this is your answer in image
Answer:
In this question, we need to evaluate the following expression i.e.
\dfrac{5\sin^230+\cos^245-4\tan^2 30}{2\sin30\cos30+\tan45}
2sin30cos30+tan45
5sin
2
30+cos
2
45−4tan
2
30
The values of following trigonometric quantities are:
\begin{gathered}\sin30=\dfrac{1}{2}\\\\\cos45=\dfrac{1}{\sqrt2}\\\\\tan 30=\dfrac{1}{\sqrt 3}\\\\\cos30=\dfrac{\sqrt3}{2}\\\\\tan45=1\end{gathered}
sin30=
2
1
cos45=
2
1
tan30=
3
1
cos30=
2
3
tan45=1
So,
\begin{gathered}=\dfrac{5\times (\dfrac{1}{2})^2+(\dfrac{1}{\sqrt2})^2-4\times (\dfrac{1}{\sqrt3})^2}{2\times \dfrac{1}{2}\times \dfrac{\sqrt3}{2}+1}\\\\=\dfrac{\dfrac{5}{4}+\dfrac{1}{2}-\dfrac{4}{3}}{\dfrac{\sqrt3}{2}+1}\\\\=\dfrac{5}{6(\sqrt 3+2)}\end{gathered}
=
2×
2
1
×
2
3
+1
5×(
2
1
)
2
+(
2
1
)
2
−4×(
3
1
)
2
=
2
3
+1
4
5
+
2
1
−
3
4
=
6(
3
+2)
5