The correct option is B tan θ + 3 cot θ =5 sec θ⇒ sin^2 θ + 3 cos^2 θ = 5 sin θ⇒ sin^2 θ + 3 (1 sin^2 θ)=5 sin θ ⇒ (sin θ + 3)(2 sin θ 1)=0 ⇒ sin θ = 3 or 1/2⇒ ...

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

Byju's Answer

Standard XII

Mathematics

Circular Measurement of Angle

If tanθ+3 θ=5...

Question

$I f t a n θ + 3 c o t θ = 5 s e c θ t h e n θ =$

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

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

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

Open in App

Solution

The correct option is B
$t a n θ + 3 c o t θ = 5 s e c θ \Rightarrow s i n^{2} θ + 3 c o s^{2} θ = 5 s i n θ \Rightarrow s i n^{2} θ + 3 (1 - s i n^{2} θ) = 5 s i n θ \Rightarrow (s i n θ + 3) (2 s i n θ - 1) = 0 \Rightarrow s i n θ = - 3 o r \frac{1}{2} \Rightarrow s i n θ = \frac{1}{2} \Rightarrow θ = n π + (- 1)^{n} \frac{π}{6}, n ϵ Z .$

Suggest Corrections

Similar questions

Q. Solve:

tan θ + 3 cot θ = 5 sec θ

Q. Solve

tan θ + 3 cot θ = 5 sec θ

\frac{cot θ}{cot θ - cot 3 θ} + \frac{tan θ}{tan θ - tan 3 θ} =

Q. Solve:

\frac{cot θ}{cot θ - cot 3 θ} + \frac{tan θ}{tan θ - tan 3 θ} = ?

Q. If

tan θ + cot θ = 4

, then the value of

{tan}^{3} θ + {cot}^{3} θ

Join BYJU'S Learning Program

If tanθ+3cotθ=5secθ then θ=

The correct option is B tanθ+3cotθ=5secθ⇒sin2θ+3 cos2θ=5sinθ⇒sin2θ+3(1−sin2θ)=5 sin θ⇒(sin θ+3)(2 sin θ−1)=0⇒sin θ=−3 or 12⇒sin θ=12⇒θ=nπ+(−1)nπ6,nϵZ.

$I f t a n θ + 3 c o t θ = 5 s e c θ t h e n θ =$