the velocities of a body executing shm are 3 and 4cms^-1 when the displacements are 4 and 3cm period is
Answers
Explanation:
example, 2(x+1)=2x+22(x+1)=2x+2 is an identity equation. One way of checking is by simplifying the equation:
\begin{aligned} 2(x+1)&=2x+2\\ 2x+2&=2x+2\\ 2&=2. \end{aligned}
2(x+1)
2x+2
2
=2x+2
=2x+2
=2.
2=22=2 is a true statement. Getting this kind of form is an indicator that the equation is in fact an identity equation. If we check by substituting different numbers, we see that the above assertion is indeed true. The following are identity equations:
\begin{aligned} a(x+b)&=ax+ab\\ { (x+1) }^{ 2 }&={ x }^{ 2 }+2x+1\\ { (x+y) }^{ 2 }&={ x }^{ 2 }+2xy+{ y }^{ 2 }\\ { \sin }^{ 2 }\theta +{ \cos }^{ 2 }\theta &=1. \end{aligned}
a(x+b)
(x+1)
2
(x+y)
2
sin
2
θ+cos
2
θ
=ax+ab
=x
2
+2x+1
=x
2
+2xy+y
2
=1.
The last equation is called a trigonometric identity.
Solving identity equations:
When given an identity equation in certain variables, start by collecting like terms (terms of the same variable and degree) together. Doing this will usually pair terms one on one, thus making it easier to solve. Let's see some examples:
Given that (5x+3)-(2x+1)=ax+b(5x+3)−(2x+1)=ax+b is an algebraic identity in x,x, what are the values of aa and b?b?
First, let us simplify the identity as follows:
\begin{aligned} (5x+3)-(2x+1)&=ax+b\\ (5x-2x)+(3-1)&=ax+b\\ 3x+2&=ax+b. \end{aligned}
(5x+3)−(2x+1)
(5x−2x)+(3−1)
3x+2
=ax+b
=ax+b
=ax+b.