If sin x-y-sin x-y-a-b-a-b- then tan x-tan y is equal to

The correct option is C a/b Given, sin(x+y)/sin(x y)=a+b/a b Applying componendo and dividendo, we get sin(x+y)+sin(x y)/sin(x+y) sin(x y)=(a+b)+(a b)/(a+b) (a ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Derivatives

If sin x+y/si...

Question

$I f \frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b}, t h e n \frac{t a n x}{t a n y} i s e q u a l t o$

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b/a

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a/b

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Solution

The correct option is D
a/b

$G i v e n, \frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b} Applying componendo and dividendo, we get \frac{s i n (x + y) + s i n (x - y)}{s i n (x + y) - s i n (x - y)} = \frac{(a + b) + (a - b)}{(a + b) - (a - b)} \Rightarrow \frac{2 s i n x c o s y}{2 c o s x s i n y} = \frac{2 a}{2 b} \Rightarrow \frac{t a n x}{t a n y} = \frac{a}{b}$

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If sin(x+y)sin(x−y)=a+ba−b,then tan xtan y is equal to

The correct option is D a/b Given, sin(x+y)sin(x−y)=a+ba−bApplying componendo and dividendo, we getsin(x+y)+sin(x−y)sin(x+y)−sin(x−y)=(a+b)+(a−b)(a+b)−(a−b)⇒2 sin x cos y2 cos x sin y=2a2b⇒tan xtan y=ab

$I f \frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b}, t h e n \frac{t a n x}{t a n y} i s e q u a l t o$