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 $1-\sin^2 x$, we will follow the below steps:
Step 1: Let us apply the following Pythagorean trigonometric identity:
$1=\sin^2 x +\cos^2 x$ $\cdots (\star)$
Step 2: Now, we substitute the value of $1$ in the expression $1-\sin^2 x$. By doing so we get that
$1-\sin^2 x= (\sin^2 x +\cos^2 x)-\sin^2 x$
$=\sin^2 x +\cos^2 x-\sin^2x$
$=\cos^2 x$ Conclusion:
Thus, the formula of $1-\sin^2 x$ is equal to $\cos^2 x$.
Note that we also have that $1-\sin^2 \theta=\cos^2 \theta$ and this is obtained in a similar way as above.
sinx=0, cosx=0, tanx=0 General Solution
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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.