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Inverse Trigonometric Functions Example 01

Inverse Trigonometric Functions Example 01. Here will provide step by step solution so that the students/viewers can easily understand

Question. Solve for x in the equation: \sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{4}, where -1 \leq x \leq 1.

Solution:

Step 1: Start by recognizing the identities for inverse trigonometric functions.

    \[ \sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2} \]

Step 2: Substitute the value of \sin^{-1}(x) + \cos^{-1}(x) with \frac{\pi}{2}.

    \[ \frac{\pi}{2} = \frac{\pi}{4} \]

Step 3: Solve for x.

    \[ x = \sin\left(\frac{\pi}{4}\right) \]

Step 4: Evaluate the value of \sin\left(\frac{\pi}{4}\right).

    \[ x = \frac{\sqrt{2}}{2} \]

The solution for the equation \sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{4} is x = \frac{\sqrt{2}}{2}.

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