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

Complementary Trigonometric Ratios

Let in a ABC,...

Question

Let in a $△ A B C,$ $x, y, z$ are the lengths of perpendicular drawn from the vertices of the triangle to the opposite sides $a, b, c .$ Then the value of $\frac{c sin B + b sin C}{x} + \frac{a sin C + c sin A}{y} + \frac{b sin A + a sin B}{z}$ is equal to

Open in App

Solution

We know perpendicular distances :
$x = c sin B = b sin C, y = a sin C = c sin A, z = b sin A = a sin B \dots (i)$
Now,
$\frac{c sin B + b sin C}{x} + \frac{a sin C + c sin A}{y} + \frac{b sin A + a sin B}{z} = \frac{x + x}{x} + \frac{y + y}{y} + \frac{z + z}{z} [using (i)] = 2 + 2 + 2 = 6$

Suggest Corrections

Similar questions

△ A B C,

x, y, z

a, b, c

\frac{b x}{c} + \frac{c y}{a} + \frac{a z}{b} = \frac{a^{2} + b^{2} + c^{2}}{k},

k

R

S

△ A B C,

x, y, z

a, b, c

cot A + cot B + cot C = k (\frac{1}{x^{2}} + \frac{1}{y^{2}} + \frac{1}{z^{2}}),

k

R, r, S, Δ

△ A B C, x, y, z

A, B, C

x, y, z

A . P .

△ A B C

x, y, z

△ A B C

\frac{a}{x} + \frac{b}{y} + \frac{c}{z}

\vec{B C} + \vec{C A} + \vec{A B} = \vec{0}

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} .

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program