If sin x -3 sin x -2 y - y - n - then the absolute value of tan x - y -tan y is

Given sin x = 3sin (x + 2y) ⇒sin (x+y y) = 3 sin (x +y+y) ⇒ nbsp;sin (x + y) cos y – cos(x+y) sin y = 3[sin (x + y) cos y + cos(x+y) sin y] ⇒ –2 sin (x+y ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If sin x =3 s...

Question

If $sin x = 3 sin (x + 2 y), y \neq n π$ , then the absolute value of $\frac{tan (x + y)}{tan y}$ is

Open in App

Solution

Given
$sin x = 3 sin (x + 2 y) \Rightarrow sin (x + y - y) = 3 sin (x + y + y) \Rightarrow sin (x + y) cos y - cos (x + y) sin y = 3 [sin (x + y) cos y + cos (x + y) sin y] \Rightarrow - 2 sin (x + y) cos y = 4 cos (x + y) sin y \Rightarrow - tan (x + y) = 2 tan y ∴ \frac{tan (x + y)}{tan y} = - 2$
So, absolute value will be $2$

Suggest Corrections

Similar questions

Q. If

\frac{sin (x + y)}{sin (x - y)} = \frac{a + b}{a - b}

, then the value of

\frac{tan x}{tan y}

equals

Q. If

\frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b},

, then show that

\frac{t a n x}{t a n y} = \frac{a}{b},

Q. Prove that:

\frac{sin (x + y)}{sin (x - y)} = \frac{tan x + tan y}{tan x - tan y}

Q. Show that

\frac{sin (x + y)}{sin (x - y)} = \frac{tan x + tan y}{tan x - tan y}

Q. If

\frac{s i n (x + y)}{s i n (x - y)} = \frac{a + b}{a - b}, then \frac{t a n x}{t a n y} =

Join BYJU'S Learning Program

If sinx=3sin(x+2y),y≠nπ, then the absolute value of tan(x+y)tany is

Given sinx=3sin(x+2y)⇒sin(x+y−y)=3sin(x+y+y)⇒sin(x+y)cosy–cos(x+y)siny =3[sin(x+y)cosy+cos(x+y)siny]⇒–2sin(x+y)cosy=4cos(x+y)siny⇒−tan(x+y)=2tany∴tan(x+y)tany=−2 So, absolute value will be 2

If $sin x = 3 sin (x + 2 y), y \neq n π$ , then the absolute value of $\frac{tan (x + y)}{tan y}$ is