Question

To simplify the expression $1 - {\sin ^2}x$.

Answer 1

Hint: In this question we will use the concept of trigonometry. In this question, we will use the stand identity of the trigonometry to simplify the given expression that involves the same trigonometric function.

Complete step by step solution:
In this question, we will first discuss the trigonometry ratios as these are the ratios between edges of the right-angle triangle. There are six trigonometric ratios sin, cos, tan, cosec, sec, cot. Sine function defined as the ratio of perpendicular to the hypotenuse. Cos function is defined as the ratio of base to the hypotenuse. Tan function is defined as the ratio of perpendicular to the base. The reciprocal of these functions define cosec, sec, and cot respectively.
As we know that it is used in oceanography to find the depth and tides in the ocean. It is also used in calculus and algebra. The right-angled triangle having three sides use the Pythagorean concept to find the length of the side. It is widely used in many fields such as Physics, in making designs of roads and buildings.
To simplify the expression $1 - {\sin ^2}x$ we will use the identity,
$ \Rightarrow {\cos ^2}x + {\sin ^2}x = 1$.
Now, we rearrange the identity according to given expression as,
$\therefore {\cos ^2}x = 1 - {\sin ^2}x$.

Therefore, the value of $1 - {\sin ^2}x$ is ${\cos ^2}x$.

Note: As we know that identity is equality relating one mathematical expression to another. In trigonometry, identity involves trigonometry functions to relate them to each other. They are used to solve trigonometry and geometrical problems. It enables us to solve complicated expressions.