If a cos 2 - b sin 2 - c has - and -as its solution- then the value of tan-tan- isA- 2 b-2 b- C- c-a-a bD- b-c-a

The correct option is B a cos 2θ+b sin 2θ=c ⇒ a (1 tan^2 θ/1+tan^2 θ)+b 2 tan θ/1+tan^2 θ=c ⇒ a atan^2 θ+2b tan θ=c+c tan^2 θ ⇒ (a+c)tan^2 θ+2b tan θ+(a c)=0 ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If a cos 2 θ+...

Question

If $a c o s 2 θ + b s i n 2 θ = c h a s α a n d β$
as its solution, then the value of $t a n α + t a n β$ is

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Solution

The correct option is B
$a c o s 2 θ + b s i n 2 θ = c$
$\Rightarrow a (\frac{1 - t a n^{2} θ}{1 + t a n^{2} θ}) + b \frac{2 - t a n θ}{1 + t a n^{2} θ} = c$
$\Rightarrow a - a t a n^{2} θ + 2 b t a n θ = c + c t a n^{2} θ$
$\Rightarrow - (a + c) t a n^{2} θ + 2 b t a n θ + (a - c) = 0$
$∴ t a n α + t a n β = - \frac{2 b}{- (c + a)} = \frac{2 b}{c + a} .$

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If a cos 2θ+b sin 2θ=c has α and β as its solution, then the value of tan α+tan β is

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If $a c o s 2 θ + b s i n 2 θ = c h a s α a n d β$
as its solution, then the value of $t a n α + t a n β$ is