Find the values of λ and μ in the expression.
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3x4 + λx³ + 12x² + μx + 4
is (i) exactly divisible by (x-1) and (ii) leaves remainder 18 when divided by (x + 2).
Prove by induction that, for positive integral values of n,
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(cos θ + i sin θ)n = cos nθ + i sin nθ.
Prove that:
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cos5 θ = 1/16(cos 5θ – 5 cos 3θ + 10 cos θ)
Prove that:
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Sin5 θ = 1/16(sin 5θ - 5 sin 3θ + 10 sin θ)
Show that :
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tan 5θ = (5 tan θ - 10 tan³ θ + tan5 θ)/(1 - 10 tan² θ + 5 tan4 θ)
Show that:
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tan 4θ = (4t - 4t³)/(1 - 6t² + t4 )
where t = tan θ.
Hence find the roots of the equation
t4 + 4t³ - 6t² - 4t + 1 = 0, correct to three significant figures.
Show that :
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tan 4θ = (4 tanθ - 4 tan³ θ)/(1 - 6 tan² θ + tan4 θ).
Prove that tan 3θ = (3 tanθ – tan³ θ)/(1 – 3 tan² θ)
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