SOLUTION: Verify the identity using Aultiple-Angle Trigonometric formulas.
1a) cos^(4)x-sin^(4)x=cos2x
1b) tanθ+cotθ=2csc2θ
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Question 148912: Verify the identity using Aultiple-Angle Trigonometric formulas.
1a) cos^(4)x-sin^(4)x=cos2x
1b) tanθ+cotθ=2csc2θ
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
cos^4(x) - sin^4(x) = cos(2x)
cos^4(x) - sin^4(x) = 2cos^2(x) - 1
( cos^2(x) + sin^2(x) )( cos^2(x) - sin^2(x) ) = 2cos^2(x) - 1
( cos^2(x) + 1 - cos^2(x) )( cos^2(x) - ( 1 - cos^2(x) ) ) = 2cos^2(x) - 1
( 1 )( 2cos^2(x) - 1 ) = 2cos^2(x) - 1
~
tan(θ) + cot(θ) = 2csc(2θ)
tan(θ) + cot(θ) = 2/sin(2θ)
tan(θ) + cot(θ) = 1/sin(θ)cos(θ)
sin(θ)/cos(θ) + cos(θ)/sin(θ) = 1/sin(θ)cos(θ)
sin^2(θ)/cos(θ)sin(θ) + cos^2(θ)/sin(θ)cos(θ) = 1/sin(θ)cos(θ)
( sin^2(θ) + cos^2(θ) )/sin(θ)cos(θ) = 1/sin(θ)cos(θ)
1/sin(θ)cos(θ) = 1/sin(θ)cos(θ)
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