JEE MATHEMATICS MCQ: PROPERTIES OF TRIANGLES

1 Easy

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Application +4 | -1

\mathrm{A}, \mathrm{B}, \mathrm{C}

are the angles of a triangle, then

\sin ^2 A+\sin ^2 \mathrm{~B}+\sin ^2 \mathrm{C}-2 \cos \mathrm{A} \cos \mathrm{B} \cos \mathrm{C}=

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Correct option: B

Option B (2) is correct because the trigonometric expression simplifies to 2 using trigonometric identities and the fact that A, B, and C are angles of a triangle.

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{p_1},{p_2},{p_3}

are altitudes of a

\Delta \;ABC

drawn from the vertices

A,B,C

and

\Delta

the area of the triangle, then

p_1^{ - 2} + p_2^{ - 2} + p_3^{ - 2}

is equal to If the sides of the triangles are

5k,\;6k,\;5k

and radius of incircle is 6, the value of

k

is equal to In a

\Delta \,ABC

, if

a = \left( {b - c} \right)\sec \theta

, then

\frac{{2\,\sqrt {bc} }}{{b - c}}\,\,\sin \,\,\frac{A}{2} =

\Delta \;ABC,\frac{{b + c}}{a}

is equal to If

\Delta = {a^2} - {\left( {b - c} \right)^2}

, where

\Delta

is the area of

\Delta \;ABC

, then

\tan A

is equal to If

A

is the area and

2 s

is the sum of the sides of a triangle, then