perplexus.info :: Just Math : sine of double angle

sine of double angle (Posted on 2024-12-31)

Compute sin(2θ) if sin⁴(θ-15)+cos⁴(θ+15)=1. (All angles are in degrees)

No Solution Yet Submitted by Danish Ahmed Khan

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Solution the long way

Comment 1 of 1

Doing the algebra with Desmos

Rewrite the LHS using the angle sum/differences formulas [4]

Expand the binomials [5]

Simplify (with help from Wolfram) all the sin(15)^3*cos(15) etc [6]

Simplify into a quadratic in terms of sin(2x) (a bit more Wolfram) [7],[8]

Set equal to 1 and solve the quadratic

sin(2x)^2+4sin(2x)+1=0

sin(2x)=-2 +/- sqrt(3)

https://www.desmos.com/calculator/ytn16aqm8b

Posted by Jer on 2024-12-31 14:12:18

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