Math Problem Statement
If (sinθ+cosθ)/(sinθcosθ)=3, determine the value of sin^4(θ)cos^4 (θ) without the use of a calculator.
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Pythagorean Identity
Formulas
Pythagorean identity: \(\sin^2 \theta + \cos^2 \theta = 1\)
Theorems

Suitable Grade Level
Advanced High School
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Simplifying cos^4(θ)  sin^4(θ) using Trigonometric Identities
Trigonometric Identity: cos^4θ + sin^4θ = 1  2cos^2θsin^2θ
Trigonometric Simplification: 1  2sin^2(θ) + sin^4(θ)
Trigonometric Expression Simplification: sin(θ) + cos(θ) Squared