Evaluate 1-2cos^2 25/1-2sin^2 65

  • Thread starter Thread starter lionely
  • Start date Start date
  • Tags Tags
    Angle
Click For Summary
SUMMARY

The discussion focuses on evaluating the expression 1 - 2cos²(25°) / (1 - 2sin²(65°)). Participants clarify that the angles are in degrees and emphasize the importance of using trigonometric identities, particularly the double angle identities for sine and cosine. The final conclusion reached is that the expression simplifies to 1, confirming the correct application of these identities in the evaluation process.

PREREQUISITES
  • Understanding of trigonometric identities, specifically double angle identities.
  • Familiarity with sine and cosine functions in degrees.
  • Basic knowledge of algebraic manipulation of trigonometric expressions.
  • Ability to apply fundamental trigonometric formulas such as cos²x + sin²x = 1.
NEXT STEPS
  • Study the double angle identities for sine and cosine functions.
  • Practice evaluating trigonometric expressions without a calculator.
  • Explore the addition formulas for sine and cosine.
  • Review common trigonometric identities and their applications in problem-solving.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their skills in evaluating trigonometric expressions without computational tools.

lionely
Messages
574
Reaction score
2
Evaluate
1-2cos2 25/ 1 -2sin2 65

The attempt at a solution

1-2cos^50= sin^2 50
so sin^2 50 / cos^2 130I'm stuck and most likely this isn't correct.
 
Last edited:
Physics news on Phys.org
What you have written makes no sense at all. Surely you don't believe that 2sin(x)= sin(2x)? What trig identities do you know?

Are we to assume that the "25" and "65" are in degrees? Why not just use a calculator to evaluate them?
 
Oh I can't use a calculator, that's what it says in the instructions. the identities I know are

cos^2x + sin^2 = 1
1+tan^2x = sec^2 x
cot^2x + 1 = cosec^2x

The addition formulae and the double angle formulae

yes they are in degrees.
 
I got it I think. I'm sorry for being stupid, I forgot about the double angle identities for sin^2 and cos^2

I substitued them in and I got 1. Which I think is correct.
 

Similar threads

  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
10
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
17
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K