SOLUTION: I simply dont understand how to switch from the identites and solve these sort of questions... Prove the following identities: Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1 CosA -si

Algebra ->  Trigonometry-basics -> SOLUTION: I simply dont understand how to switch from the identites and solve these sort of questions... Prove the following identities: Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1 CosA -si      Log On


   

Question 836065: I simply dont understand how to switch from the identites and solve these sort of questions...
Prove the following identities:
Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1
CosA -sinA/ cos A+sinA = 1-2sinAcosA/1-2sin^2A
CosA/sqroot(1+tanA) + sinA/ sqroot (1+cot^2 A) =1
Please help, thank you,!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Prove the following identities:
Cos^4 A + sin^4 A + 2sin^2 Ax cos^2 A =1
Factor:
(cos^2+sin^2)(cos^2+sin^2) = 1
1*1 = 1
1 = 1
--------------------------------------------------
CosA -sinA/ cos A+sinA = 1-2sinAcosA/1-2sin^2A
Left side: Multiply numerator and denominator by cos-sin
Right side: In place of "1" put sin^2+cos^2
---
(cos-sin)^2/(cos^2-sin^2) = [sin^2 -2sin*cos +cos^2]/(1-2sin^2)
-------
Notice that the numerators are the same
Notice that the denominators are the same
-------
(cos^2-2cos*sin+sin^2)/(1-2sin^2) = (cos^2-2sin*cos+sin^2)/(1-2sin^2
==================================
Cheers,
Stan H.
------