Question

What is the value of ${\sin ^2}\left( {\dfrac{\pi }{2}} \right) - \cos \pi$ ?

Answer 1

Hint : In order to find the value of the equation given first check whether the equation can be more simplified to its lowest version or not and we see that it cannot be solved or simplified more. Therefore, we just have to put the value of $\sin \left( {\dfrac{\pi }{2}} \right)$ and $\cos \pi$ then solve the equation and get the results.

Complete step by step solution:
We are given the equation ${\sin ^2}\left( {\dfrac{\pi }{2}} \right) - \cos \pi$ .
Since, we know the value of $\sin \left( {\dfrac{\pi }{2}} \right)$ and $\cos \pi$ so simply we can put the value in the above equation.
From the trigonometric values,
Value of $\sin \left( {\dfrac{\pi }{2}} \right) = 1$ and value of $\cos \pi = - 1$ .
For further results just put the value in the equation and we get:
${\left( {\sin \left( {\dfrac{\pi }{2}} \right)} \right)^2} - \cos \pi = {\left( 1 \right)^2} - \left( { - 1} \right) = 1 + 1 = 2$
Therefore, The value of ${\sin ^2}\left( {\dfrac{\pi }{2}} \right) - \cos \pi$ =2
So, the correct answer is “2”.

Note : Some of the trigonometric values used in mathematical calculations are: $\sin \left( {\dfrac{\pi }{2}} \right) = 1$
$\cos \pi = - 1$
$\cos 0 = 1$
$\sin 0 = 0$ and etc.
The values which are known to us can be solved directly just be putting the values.
The angles whose values are not known, can be found using a calculator.
x-axis is the line for cos and the values of cos is $1 or - 1$ in the axis and value of sine is zero, whereas y-axis is the line for sine in which the values of cos is zero.