Simplify the Expression 1-sin^2x | 1-sin^2x Formula, Identity

The value of the expression 1-sin^2(x) is equal to cos^2(x). In this post, we will find the formula of 1-sin^2x.

1-sin²x Formula

To simplify the expression 1 – sin²x, we will follow the below steps:

Step 1: Let us apply the following Pythagorean trigonometric identity:

1 = sin²x + cos²x 

Step 2: Now, we substitute the above value of 1 in the expression 1 – sin²x. By doing so we get that

1 – sin²x = (sin²x + cos²x) – sin²x

= sin²x + cos²x – sin²x

= cos² x

Thus, the formula of 1-sin²x is equal to cos²x .

Note that we also have that $1-{\sin }^2\theta ={\cos }^2\theta$ and this is obtained in a similar way as above.

Also Read:

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Question-Answer on 1-sin²x Formula

Question 1: Find the value of $1-{\sin }^2{60}^{\circ }$

Answer:

From the above, we get the value of $1-{\sin }^{2}x$ which is equal to ${\cos }^{2}x$. In this formula, we put $x={60}^{\circ }$. So we get that

$1-{\sin }^2{60}^{\circ }$

$={\cos }^2{60}^{\circ }$

$=({\displaystyle \frac{1}{2}}{)}^2$

$=1/4$ as we know that $\cos {60}^{\circ }=1/2$.

Thus, the value of $1-{\sin }^2{60}^{\circ }$ is equal to $1/4$.

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