this is for proving identies and its fustrating i can't solve this one question! lol
x=feta
(btw the first part is supposed to be divided by the bottom)
1 + 2sinxcosx + sinxcosx
sinx + cosx
(1 + 2sinxcosx / sinx + cosx) + sinxcosx
oh shoot i wrote it wrong
its:
1 + 2sinxcosx = sinxcosx
sinx + cosx
I believe you still wrote it wrong.
it should be
(1 + 2sinxcosx)/(sinx + cosx) = sinx + cosx
to prove this, recall that sin^2 x + cos^2 x = 1
so replace the 1 with that.
LS = (sin^2 x + 2sinxcosx + cos^2 x)/(sinx + cosx)
= (sinx + cosx)^2/(sinx + cosx)
= sinx + cosx
= RS
thank you:)
To solve this question, we need to simplify the given expression step by step. Let's break it down:
Step 1: Simplify the numerator of the expression.
In the numerator, we have (1 + 2sinxcosx + sinxcosx). We can factor out sinx from the terms by using the distributive property:
sinx(1 + 2cosx + cosx)
Now we can simplify the expression further:
sinx(1 + 3cosx)
Step 2: Simplify the denominator of the expression.
The denominator is (sinx + cosx).
Step 3: Combine the numerator and denominator.
Now we can rewrite the entire expression as:
(sinx(1 + 3cosx)) / (sinx + cosx) + sinxcosx
Step 4: Simplify further.
Let's simplify the expression inside the parentheses:
sinx(1 + 3cosx) = sinx + 3sinxcosx
Now the entire expression becomes:
(sinx + 3sinxcosx) / (sinx + cosx) + sinxcosx
And that is the simplified form of the given expression.
Note: It's important to note that proving identities often involves manipulating expressions based on the known trigonometric identities. It helps to be familiar with these identities so that you can spot opportunities for simplification.