Question:
The value of
\[
1+\cot^2 30^\circ-\sec^2 45^\circ
\]
is
The value of
\[
1+\cot^2 30^\circ-\sec^2 45^\circ
\]
is
Show Hint
Memorize the standard trigonometric values for \(30^\circ\), \(45^\circ\), and \(60^\circ\). They are frequently used in simplification problems.
Updated On: Jun 26, 2026
- \(\dfrac{1}{4}\)
- \(\dfrac{1-\sqrt{3}}{2}\)
- \(2\)
- \(0\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Use standard trigonometric values.
We know that \[ \cot 30^\circ=\sqrt{3} \] and \[ \sec 45^\circ=\sqrt{2} \]
Step 2: Square the values.
\[ \cot^2 30^\circ=(\sqrt{3})^2=3 \] and \[ \sec^2 45^\circ=(\sqrt{2})^2=2 \]
Step 3: Substitute in the expression.
\[ 1+\cot^2 30^\circ-\sec^2 45^\circ \] \[ =1+3-2 \] \[ =2 \]
Step 4: Final conclusion.
Therefore, \[ \boxed{2} \]
We know that \[ \cot 30^\circ=\sqrt{3} \] and \[ \sec 45^\circ=\sqrt{2} \]
Step 2: Square the values.
\[ \cot^2 30^\circ=(\sqrt{3})^2=3 \] and \[ \sec^2 45^\circ=(\sqrt{2})^2=2 \]
Step 3: Substitute in the expression.
\[ 1+\cot^2 30^\circ-\sec^2 45^\circ \] \[ =1+3-2 \] \[ =2 \]
Step 4: Final conclusion.
Therefore, \[ \boxed{2} \]
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