Answer :

Given,


The length two sides of a triangle are ‘a’ and ‘b’


Angle between the sides ‘a’ and ‘b’ is θ.


The area of the triangle is maximum.



Let us consider,


The area of the ΔPQR is given be


---- (1)


For finding the maximum/ minimum of given function, we can find it by differentiating it with θ and then equating it to zero. This is because if the function A (θ) has a maximum/minimum at a point c then A’(c) = 0.


Differentiating the equation (1) with respect to θ:



---- (2)


[Since ]


To find the critical point, we need to equate equation (2) to zero.



Cos θ = 0



Now to check if this critical point will determine the maximum area, we need to check with second differential which needs to be negative.


Consider differentiating the equation (2) with θ :



----- (2)


[Since ]


Now let us find the value of



As , so the function A is maximum at


As the area of the triangle is maximum when


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