Master Proofs with Ease: Solving Tricky Trigonometric Equations

Thread starter yvette25
Start date Nov 12, 2007
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Proofs

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SUMMARY

The discussion focuses on solving three trigonometric equations: proving that sin(3x) equals sin(x)(3 - 4sin²(x)), simplifying the expression tan(x) + sin(x)/(2tan(x)) to cos²(x/2), and manipulating cot(2x) using the identity cot(x) = 1/tan(x). Participants emphasize rewriting sin(3x) as sin(2x + x) and suggest simplifying the second and third equations into sine and cosine forms for easier manipulation.

PREREQUISITES

Understanding of trigonometric identities, specifically sin and cos functions.
Familiarity with the sine addition formula.
Knowledge of cotangent and tangent functions.
Ability to manipulate algebraic expressions involving trigonometric functions.

NEXT STEPS

Study the sine addition formula in depth.
Learn how to convert between cotangent and tangent functions effectively.
Practice simplifying complex trigonometric expressions into sine and cosine forms.
Explore advanced trigonometric identities and their proofs.

USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their skills in solving trigonometric equations.

Nov 12, 2007

yvette25

Homework Statement

prove:
sin3x = sinx (3-4sin^2x)

tanx+sinx/2tanx = cos^2(x/2)

cot2x = (cot^2 x-1)/(2cotx)

Last edited: Nov 12, 2007

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Nov 12, 2007

rock.freak667

Homework Helper

...where is your attempt?
But anyhow...for the first one...rewrite sin3x as sin(2x+x)

and well for the second and third ones..try simplifying it into sin and cos only , for the last one...remember that cot(x)=1/tan(x)