Explain how to do this with steps please.
1. Simplify cos(x-y)+cos(x+y)/cosx
Formula: cosxcosy= cos(x+y)+cos(x-y)/2
cos(x-y)+cos(x+y)/cosx
=cosxcosy/2cosx
To simplify the expression cos(x-y) + cos(x+y)/cosx, we can make use of the formula cosxcosy = cos(x+y) + cos(x-y)/2.
Step 1: Apply the formula cosxcosy = cos(x+y) + cos(x-y)/2 to the expression. This gives us:
cos(x-y) + cos(x+y) / cosx = cosx*cosy / 2cosx
Step 2: Simplify the expression by canceling out the cosx term in the numerator and denominator:
cosx*cosy / 2cosx = cosy / 2
So, the simplified form of the given expression is cosy/2.
To simplify the expression cos(x-y) + cos(x+y) / cos(x), we can use the formula cos(x+y) + cos(x-y) = 2cos(x)cos(y).
Here are the steps to simplify the expression:
Step 1: Write the given expression:
cos(x-y) + cos(x+y) / cos(x)
Step 2: Use the formula cos(x+y) + cos(x-y) = 2cos(x)cos(y) to simplify the numerator:
= 2cos(x)cos(y) / cos(x)
Step 3: Cancel out the cos(x) terms in the numerator and denominator:
= 2cos(y)
Therefore, the simplified expression is 2cos(y).