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.
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.
Question-Answer on 1-sin2x Formula
Question 1: Find the value of $1-\sin^2 60^\circ$
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
$=1/4$ as we know that $\cos 60^\circ =1/2$.
Thus, the value of $1-\sin^2 60^\circ$ is equal to $1/4$.
Q1: What is the formula of 1-sin2x?
Answer: The formula is 1-sin2x=cos2x.