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Maths-

General

Easy

Question

If $cos invisible function application B cos invisible function application C plus sin invisible function application B sin invisible function application C sin to the power of 2 end exponent invisible function application A equals 1 comma$ then triangle $A B C$ is

Isosceles and right angled
Equilateral
Isosceles whose equal angles are greater than $π / 4$
None

The correct answer is: Isosceles and right angled

Given, $cos invisible function application B cos invisible function application C plus sin invisible function application B sin invisible function application C sin to the power of 2 end exponent invisible function application A equals 1$ (i)
Now, we know that $sin to the power of 2 end exponent invisible function application A less or equal than 1$ (ii)
Also, $sin invisible function application B$ and $sin invisible function application C$ are positive
$rightwards double arrow sin invisible function application B sin invisible function application C sin to the power of 2 end exponent invisible function application A less or equal than sin invisible function application B sin invisible function application C$ (iii)
$rightwards double arrow 1 minus cos invisible function application B cos invisible function application C less or equal than sin invisible function application B sin invisible function application C$ , [by using Eq.(i) ]
$rightwards double arrow cos invisible function application open parentheses B minus C close parentheses greater or equal than 1 blank rightwards double arrow cos invisible function application open parentheses B minus C close parentheses equals 1 blank rightwards double arrow B minus C equals 0 blank rightwards double arrow B equals C$
Also, $sin to the power of 2 end exponent invisible function application A equals 1 comma blank i. e. comma blank A equals pi divided by 2.$ Hence, the triangle is right-angled isosceles

Related Questions to study

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