If 5 sin-3 sin -2 -0- then the tan - is equal to

The correct option is C 4 tan β We have, 5 sin α = 3 sin (α + 2 β) ⇒ 5/3=sin (α + 2 β)/sin α ⇒ 5 3/5+3=sin (α + 2 β) sin α/sin (α + 2 β) + sin α (Using ...

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

Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

If 5 sinα=3 s...

Question

If 5 sin $α = 3 s i n (α + 2 β) \neq 0$ , then the $t a n (α + β)$ is equal to

$2 t a n β$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$3 t a n β$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$4 t a n β$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$6 t a n β$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$4 t a n β$

We have,

$5 s i n α = 3 s i n (α + 2 β) \Rightarrow \frac{5}{3} = \frac{s i n (α + 2 β)}{s i n α}$

$\Rightarrow \frac{5 - 3}{5 + 3} = \frac{s i n (α + 2 β) - s i n α}{s i n (α + 2 β) + s i n α}$ (Using componendo and dividendo)

$\Rightarrow \frac{2}{8} = \frac{s i n (α + 2 β) - s i n α}{s i n (α + 2 β) + s i n α} \Rightarrow \frac{1}{4} = \frac{2 c o s \frac{α + 2 β + α}{2} s i n \frac{α + 2 β - α}{2}}{2 s i n \frac{α + 2 β + α}{2} c o s \frac{α + 2 β - α}{2}} \Rightarrow \frac{1}{4} = \frac{c o s (α + β) s i n β}{s i n (α + β) c o s β} \Rightarrow \frac{1}{4} c o t (α + β) t a n β \Rightarrow \frac{1}{t a n (α + β)} t a n β ∵ t a n (α + β) = 4 t a n β$

Suggest Corrections

Similar questions

Q. If

5 \sin α = 3 \sin (α + 2 β) \neq 0

, then

\tan (α + β)

is equal to
(a)

2 \tan β

(b)

3 \tan β

(c)

4 \tan β

(d)

6 \tan β

Q. If

3 s i n α = 5 s i n β

, then

\frac{tan \frac{α + β}{2}}{tan \frac{α - β}{2}}

is equal to

Q. If

3 sin α = 5 sin β

, then

\frac{tan \frac{α + β}{2}}{tan \frac{α - β}{2}} =

Q. If

3 sin α = 5 sin β

, then:

tan (\frac{α + β}{2}) + tan (\frac{α - β}{2})

Q. If

tan α = \frac{4}{15} (0 < α < 90^{\circ})

, then the value of

\frac{5 sin α + 7 cos α}{6 cos α - 3 sin α}

Join BYJU'S Learning Program

If 5 sin α=3 sin (α+2β)≠0, then the tan(α+β) is equal to

If 5 sin $α = 3 s i n (α + 2 β) \neq 0$ , then the $t a n (α + β)$ is equal to