Question

\(\sin^2 90^\circ - \tan^2 45^\circ = \)

• A. 1
• B. \(\frac{1}{2}\)
• C. \(\frac{1}{\sqrt{2}}\)
• D. 0

Hint:

Be careful with the notation \(\sin^2 \theta\), which means \((\sin \theta)^2\). First find the value of the trigonometric function, then apply the exponent.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to evaluate the given trigonometric expression by substituting the known values of \(\sin 90^\circ\) and \(\tan 45^\circ\).

Step 2: Key Formula or Approach:
We will use the standard trigonometric values:
\[ \sin 90^\circ = 1 \] \[ \tan 45^\circ = 1 \]

Step 3: Detailed Explanation:
The expression is \(\sin^2 90^\circ - \tan^2 45^\circ\).
This can be written as \((\sin 90^\circ)^2 - (\tan 45^\circ)^2\).
Substitute the known values:
\[ = (1)^2 - (1)^2 \] \[ = 1 - 1 \] \[ = 0 \]

Step 4: Final Answer:
The value of the expression is 0.