cot sqaure 30 degree 2 cos square 30 degree - 3/4 sin square 30 degree + 2 cos square 90 degree
Answers
Answer:
cot
2
30
∘
−2cos
2
30
∘
−
4
3
sec
2
45
∘
+
4
1
csc
2
30
∘
=1
Step-by-step explanation:
Given : Expression \cot^2 30^\circ-2\cos^2 30^\circ-\frac{3}{4}\sec^2 45^\circ+\frac{1}{4}\csc ^2 30^\circcot
2
30
∘
−2cos
2
30
∘
−
4
3
sec
2
45
∘
+
4
1
csc
2
30
∘
To find : Simplify the expression ?
Solution :
Using trigonometric values,
\cot 30^\circ=\sqrt{3}cot30
∘
=
3
\cos 30^\circ=\frac{\sqrt{3}}{2}cos30
∘
=
2
3
\sec 45^\circ=\sqrt2sec45
∘
=
2
\csc 30^\circ=2csc30
∘
=2
Substitute the value in the expression,
=(\sqrt{3})^2-2(\frac{\sqrt{3}}{2})^2-\frac{3}{4}(\sqrt2)^2+\frac{1}{4}(2)^2=(
3
)
2
−2(
2
3
)
2
−
4
3
(
2
)
2
+
4
1
(2)
2
=3-2(\frac{3}{4})-\frac{3}{4}(2)+\frac{1}{4}(4)=3−2(
4
3
)−
4
3
(2)+
4
1
(4)
=3-\frac{3}{2}-\frac{3}{2}+1=3−
2
3
−
2
3
+1
=4-\frac{6}{2}=4−
2
6
=4-3=4−3
=1=1
Therefore, \cot^2 30^\circ-2\cos^2 30^\circ-\frac{3}{4}\sec^2 45^\circ+\frac{1}{4}\csc ^2 30^\circ=1cot
2
30
∘
−2cos
2
30
∘
−
4
3
sec
2
45
∘
+
4
1
csc
2
30
∘
=1
Hope it helps you
Mark me brainlist