#1
(1/sinx)(sin^2x + cos^2x(sinx/cosx) )/(sinx + cosx)
= (sinx + cosx)/(sinx+cosx)
= 1
Reiny helped with this question but I don't how Reiny did it.
Please explain
nevermind I figured it out
To help explain the steps, let's break down the expression step by step:
Given expression: (1/sinx)(sin^2x + cos^2x(sinx/cosx) )/(sinx + cosx)
Step 1: Simplify the expression within the parentheses
sin^2x + cos^2x(sinx/cosx)
= sin^2x + (sinx/cosx) * cos^2x
Step 2: Simplify the term (sinx/cosx) * cos^2x using the Rule of Exponents
= sin^2x + sinx * cosx
Step 3: Combine the like terms in the expression (sin^2x + sinx * cosx)
= sinx(sin^x + cosx)
Step 4: Simplify the expression within the parentheses (sin^x + cosx)
= (sinx + cosx)
Next, let's rewrite the original expression using this simplified form:
(1/sinx) * (sinx + cosx) / (sinx + cosx)
Step 5: Simplify the expression (sinx + cosx) / (sinx + cosx)
= 1
Finally, we are left with:
(1/sinx) * 1
Since any number divided by itself is equal to 1, we get the final answer of 1.
Therefore, the given expression simplifies to 1.