Solve the following trigonometric equation: $sin^2 x + cos^2 x = 1$, where $x$ is an acute angle.

Q: Solve the following trigonometric equation: $sin^2 x + cos^2 x = 1$, where $x$ is an acute angle.

Step 1: Recall the Pythagorean Identity\nThe Pythagorean identity states that for any angle $x$, $sin^2 x + cos^2 x = 1$. This identity is a fundamental concept in trigonometry and is used to relate the sine and cosine functions. Step 2: Analyze the Given Equation\nThe given equation is $sin^2 x + cos^2 x = 1$. Since the Pythagorean identity states that $sin^2 x + cos^2 x = 1$, we can conclude that the given equation is an identity and is true for all values of $x$. Step 3: Determine the Value of $x$\nSince the given equation is an identity, it is true for all values of $x$. Therefore, the value of $x$ is not restricted to any particular value. Step 4: Provide the Final Answer\nThe final answer is that the equation $sin^2 x + cos^2 x = 1$ is an identity and is true for all values of $x$.

Question

Accepted Answer

Step 1: Recall the Pythagorean Identity
The Pythagorean identity states that for any angle $x$, $sin^2 x + cos^2 x = 1$. This identity is a fundamental concept in trigonometry and is used to relate the sine and cosine functions. Step 2: Analyze the Given Equation
The given equation is $sin^2 x + cos^2 x = 1$. Since the Pythagorean identity states that $sin^2 x + cos^2 x = 1$, we can conclude that the given equation is an identity and is true for all values of $x$. Step 3: Determine the Value of $x$
Since the given equation is an identity, it is true for all values of $x$. Therefore, the value of $x$ is not restricted to any particular value. Step 4: Provide the Final Answer
The final answer is that the equation $sin^2 x + cos^2 x = 1$ is an identity and is true for all values of $x$.

CBSE · Class 10 · Mathematics · Introduction to TrigonometrySolve the following trigonometric equation: $sin^2 x + cos^2 x = 1$, where $x$ is an acute angle.

Step 1: Recall the Pythagorean Identity\nThe Pythagorean identity states that for any angle $x$, $sin^2 x + cos^2 x = 1$. This identity is a fundamental concept in trigonometry and is used to relate the sine and cosine functions.

Step 2: Analyze the Given Equation\nThe given equation is $sin^2 x + cos^2 x = 1$. Since the Pythagorean identity states that $sin^2 x + cos^2 x = 1$, we can conclude that the given equation is an identity and is true for all values of $x$.

Step 3: Determine the Value of $x$\nSince the given equation is an identity, it is true for all values of $x$. Therefore, the value of $x$ is not restricted to any particular value.

Step 4: Provide the Final Answer\nThe final answer is that the equation $sin^2 x + cos^2 x = 1$ is an identity and is true for all values of $x$.