The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).
So I'll take the left hand side and try to turn it into 
One way we can do that is through the following steps:

Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.
Answer:
x = 16.6
Step-by-step explanation:
Since we know the measure of an acute angle (31 degrees) of a right angle triangle, and of the side opposite to the angle (10), and we need to find the measure of the adjacent side "x", we use the tangent function:

which rounded to one decimal is
x = 16.6
Answer:
l = 6.00
Step-by-step explanation:
So A = l x w and P = 2l + 2w, they say they are equal to l (w) = 2l + 2w and we know that w = 3 so
3l = 2l + 2(3), so l = 6.
Answer:
(A) x=40
Step-by-step explanation:
Given: It is given that m is parallel to n.
To find: The value of x.
Proof: It is given that m is parallel to n, from the figure it can be seen that 105° and (3x-15)° forms alternate exterior angles which are equal in measure because m is parallel to n.
Thus, 
⇒
⇒
⇒
⇒
Thus, the value of x is 40, hence option A is correct.
Answer:
0.58 or 58%
Step-by-step explanation:
If the highest probability is 1, and you already have 0.42, you have to find what is left, so our equation is:
1 - 0.41 = 0.58
So the probability of getting a head is 0.58 or 58%