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

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Homework Help Overview

The discussion revolves around evaluating the expression 1 - 2cos²(25°) / (1 - 2sin²(65°), focusing on trigonometric identities and simplifications. Participants are exploring the relationships between sine and cosine functions, particularly in the context of degree measurements.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of trigonometric identities, including double angle formulas. There is an attempt to manipulate the expression, with some questioning the validity of the steps taken. Others express confusion regarding the assumptions about angle measurements and the use of calculators.

Discussion Status

The discussion is active, with participants sharing their attempts and clarifying their understanding of trigonometric identities. Some guidance has been offered regarding the use of double angle identities, though there is no explicit consensus on the correctness of the evaluations presented.

Contextual Notes

Participants are constrained by instructions that prohibit the use of calculators, which influences their approach to the problem. There is also a need to clarify the assumptions regarding the angles being in degrees.

lionely
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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:
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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.
 

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