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Cosine Rule

32. If α and...

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32. If α and β are two distinct roots of equation a cosx + b sinx = 10, then tan(α +β )/2 is equal to

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tan α

tan β

are the roots of the equation

x^{2} + a x + b = 0

then the value of

{sin}^{2} (α + β) + a sin (α + β) cos (α + β) + b {cos}^{2} (α + β)

α

β

are the roots of the equation

x^{2} + x + 2 = 0

\frac{α^{10} + β^{10}}{α^{- 10} + β^{- 10}}

α

is a root of equation

(2 sin x - cos x) (1 + cos x) = {sin}^{2} x

β

is a root of equation

3 {cos}^{2} x - 10 cos x + 3 = 0

γ

is a root of equation

1 - sin 2 x = cos x - sin x; 0 \leq α, β, γ \leq \frac{π}{2},

sin (α - β)

\frac{s i n (x - α)}{s i n (x - β)} = \frac{a}{b}, \frac{c o s (x - α)}{c o s (x - β)} = \frac{A}{B}

\neq

0, then prove that -

c o s (α - β) = \frac{a A + b B}{a B + b A} .

α, β

are different values of x satisfying a cos x + b sin x = c then

t a n (\frac{α + β}{2}) =

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