For - ABC - tan B - C -2-A- tan A -2B- B -2C- A -2D- sin A -2

The correct option is C cot A/2 In Δ ABC, ∠ A + ∠ B + ∠ C = 180^∘ ∴ ∠ B + ∠ C = 180 ∠ A or ∠ B + ∠ C/2 = 90^∘ ∠ A/2 Taking tan on both sides we get, tan ...

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

Byju's Answer

Standard IX

Mathematics

Angle Sum Property of a Triangle

For Δ ABC , t...

Question

$For Δ A B C, t a n (\frac{B + C}{2}) =$ _______.

$t a n \frac{A}{2}$

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

$s i n \frac{A}{2}$

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

$c o t \frac{B}{2}$

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

$c o t \frac{A}{2}$

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

Open in App

Solution

The correct option is D
$c o t \frac{A}{2}$

$In Δ A B C, ∠ A + ∠ B + ∠ C = 180^{\circ}$

$∴ ∠ B + ∠ C = 180 - ∠ A$

or $\frac{∠ B + ∠ C}{2} = 90^{\circ} - \frac{∠ A}{2}$

Taking tan on both sides we get,

$t a n (\frac{∠ B + ∠ C}{2}) = t a n (90 - \frac{∠ A}{2})$

$= c o t (\frac{∠ A}{2})$

$[t a n (90 - θ) = c o t θ]$

Suggest Corrections

Similar questions

Q. In

△ A B C

t a n (\frac{B + C}{2}) =

_______.

$I n Δ A B C, (a + b + c) (t a n \frac{A}{2} + t a n \frac{B}{2}) is equal to$

Q. In any

Δ A B C, \frac{a + b}{c} =

If sin A = n sin B, then $\frac{n - 1}{n + 1}$ tan $\frac{A + B}{2}$ =

Q. In a

Δ A B C

. If

tan \frac{A}{2}, tan \frac{B}{2}, tan \frac{C}{2}

are in

H . P

, then

a, b, c

are in:

Join BYJU'S Learning Program

For ΔABC, tan (B+C2)= _______.

The correct option is D cot A2 In ΔABC, ∠A+∠B+∠C=180∘ ∴ ∠B+∠C=180−∠A or ∠B+∠C2=90∘−∠A2 Taking tan on both sides we get, tan(∠B+∠C2)=tan(90−∠A2) =cot(∠A2) [tan (90−θ)=cot θ]

$For Δ A B C, t a n (\frac{B + C}{2}) =$ _______.