SOLUTION: I need help to rewrite each expression in terms of cos phata. Then simplify. 1. 2sin phata cos phata cot phata. 2. 1 + cot phata divided by cot phata ( sin phata+ cos phata) 3

Algebra ->  Trigonometry-basics -> SOLUTION: I need help to rewrite each expression in terms of cos phata. Then simplify. 1. 2sin phata cos phata cot phata. 2. 1 + cot phata divided by cot phata ( sin phata+ cos phata) 3      Log On


   

Question 198700: I need help to rewrite each expression in terms of cos phata. Then simplify.
1. 2sin phata cos phata cot phata.
2. 1 + cot phata divided by cot phata ( sin phata+ cos phata)
3. cos square root of 4 phata - sin square root of 4 phata + sin squareroot of 2 phata.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
It's really "theta" not "phata", but I like "phata" better! It's cute! I can't make a "theta" on here, so I'll use P for "phata".
I need help to rewrite each expression in terms of cosP. Then simplify.
1. 2%2ASinP%2ACosP%2ACotP

Change the CotP to CosP%2FSinP
2%2ASinP%2ACosP%2A%28CosP%2FSinP%29
Cancel the SinP's.
2%2Across%28SinP%29%2ACosP%2A%28CosP%2Fcross%28SinP%29%29
2%2ACos%5E2P

2. 1 + cot phata divided by cot phata ( sin phata+ cos phata)
%28++%281%2BCotP%29%2FCotP++%29%28SinP%2BCosP%29+
Change both CotP's to CosP%2FSinP
%28++%281%2BCosP%2FSinP%29%2F%28CosP%2FSinP%29++%29%28SinP%2BCosP%29+
Change the 1 to SinP%2FSinP
%28++%28SinP%2FSinP%2BCosP%2FSinP%29%2F%28CosP%2FSinP%29++%29%28SinP%2BCosP%29+
+%28%28%28SinP%2BCosP%29%2FSinP%29%2F%28CosP%2FSinP%29+%29%28SinP%2BCosP%29+
Invert and multiply:
%28%28++%28SinP%2BCosP%29%2FSinP%29%2A%28SinP%2FCosP%29++%29%28SinP%2BCosP%29+
Cancel the SinP's

+%28+%28SinP%2BCosP%29%2FCosP++%29%28SinP%2BCosP%29+
+%28+%28SinP%2BCosP%29%2FCosP++%29%28%28SinP%2BCosP%29%2F1%29+
+%28SinP%2BCosP%29%5E2%2FCosP
Now since Sin%5E2P%2BCos%5E2P=1 solved for SinP is
SinP+=+%22%22%2B-sqrt%281-Cos%5E2P%29
+%28%22%22%2B-sqrt%281-Cos%5E2P%29%2BCosP%29%5E2%2FCosP




3. cos square root of 4 phata - sin square root of 4 phata + sin squareroot of 2 phata.