MyQuestionIcon

1

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

Implicit Differentiation

If A+B+C=π,...

Question

If $A + B + C = π$ , then prove that $cot A + \frac{sin A}{sin B sin C}$ retains the same value when any two of the angles A, B, C are interchanged.

Open in App

Solution

$\frac{sin A}{sin B sin C} = \frac{sin (B + C)}{sin B sin C} = cot B + cot C$
$∴$ Given expression $= \sum cot A$ . Hence proved by symmetry.

Suggest Corrections

thumbs-up

0

Similar questions

\frac{sin (A - B)}{sin A sin B} + \frac{sin (B - C)}{sin B sin C} + \frac{sin (C - A)}{sin C sin A} = 0

Q. For any three angles A, B, C prove that

sin A + sin B + sin C - sin (A + B + C) = 4 sin {(A + B) / 2} sin {(B + C) / 2} sin {(C + A) / 2}

Q. Arrange the following values in the ascending order of their magnitudes

A + B + C = π

\frac{cos A}{sin B sin C} + \frac{cos B}{sin A sin C} + \frac{cos C}{sin A sin B} =

A + B + C = π

\sum cot A . cot B =

A + B + C = π

tan 3 A + tan 3 B + tan 3 C = 2 K tan 3 A tan 3 B tan 3 C, t h e n K =

A + B + C = π

sec A (c o s B cos C - sin B sin C) =

Q. If A, B and C are interior angles of

Δ A B C,

then Prove that :

s i n \frac{(A + C)}{2} = c o s \frac{B}{2} .

Q. If A + B + C =

π

, then prove that,

s i n \frac{A}{2} + s i n \frac{B}{2} + s i n \frac{C}{2} = 1 + 4 s i n [\frac{π - A}{4}] s i n [\frac{π - B}{4}] s i n [\frac{π - C}{4}]

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Implicit Differentiation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Implicit Differentiation

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon