If theta is an acute angle and sin theta = cos theta , find the value of 2 sin square theta - 3 cos square theta + 1/2 cot square theta.
please solve this problem if you can't understand the question you can see the image i have given and please solve this step by step.
Answers
Answer:
0
Step-by-step explanation:
For simplicity, just assume the angle theta as angle alpha.
Given that,
Solving this, we will get,
Now, to find the value of,
Simplifying this, we get,
Now, we know that,
Therefore, substituting the values, we get,
Hence, required value is 0.
Answer:
0
Step-by-step explanation:
For simplicity, just assume the angle theta as angle alpha.
Given that,
\sin( \alpha ) = \cos( \alpha )sin(α)=cos(α)
Solving this, we will get,
\begin{gathered} = > \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = 1 \\ \\ = > \tan( \alpha ) = 1 \\ \\ = > \tan( \alpha ) = \tan( \frac{\pi}{4} ) \\ \\ = > \alpha = \frac{\pi}{4} \end{gathered}
=>
cos(α)
sin(α)
=1
=>tan(α)=1
=>tan(α)=tan(
4
π
)
=>α=
4
π
Now, to find the value of,
2 { \sin }^{2} \alpha - 3 { \cos }^{2} \alpha + \frac{1}{2} { \cot }^{2} \alpha2sin
2
α−3cos
2
α+
2
1
cot
2
α
Simplifying this, we get,
2 { \sin }^{2} \frac{\pi}{4} - 3 { \cos }^{2} \frac{\pi}{4} + \frac{1}{2} { \cot }^{2} \frac{\pi}{4}2sin
2
4
π
−3cos
2
4
π
+
2
1
cot
2
4
π
Now, we know that,
\sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} }sin(
4
π
)=
2
1
\cos( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} }cos(
4
π
)=
2
1
\cot( \frac{\pi}{4} ) = 1cot(
4
π
)=1
Therefore, substituting the values, we get,
\begin{gathered} = 2 {( \frac{1}{ \sqrt{2} }) }^{2} - 3 {( \frac{1}{ \sqrt{2} }) }^{2} + \frac{1}{2} {(1)}^{2} \\ \\ = 2 \times \frac{1}{2} - 3 \times \frac{1}{2} + \frac{1}{2} \times 1 \\ \\ = 1 - \frac{3}{2} + \frac{1}{2} \\ \\ = \frac{2 - 3 + 1}{2} \\ \\ = \frac{3 - 3}{2} \\ \\ = \frac{0}{2} \\ \\ = 0\end{gathered}
=2(
2
1
)
2
−3(
2
1
)
2
+
2
1
(1)
2
=2×
2
1
−3×
2
1
+
2
1
×1
=1−
2
3
+
2
1
=
2
2−3+1
=
2
3−3
=
2
0
=0
hence your anger is 0