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If alpha + beta = 90° , then find the maximum and minimum value of sin alpha sin beta

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Answer 1

Your answer is --

Let, alpha = a

beta = b

Given,

a+b = 90°

=> a = 90° - b

Now,

sin(a) sin(b) = sin(90° - b) sin(b)

= cos(b) sin(b) .......(1)

Now, using the trigonometric identities

sin(2b) = 2sin(b) cos(b)

divide both side by 2 , we get

sin(2b)/2 = sin(b) cos(b) .....(2)

So, from (1) & (2)

sin(a) sin(b) = sin(2a)/2

we know that the maximum value of sine function is 1.

So, maximum value of sin(2a)/2 is 1/2

Therefore, maximum value of
sin(a) sin(b) is 1/2

Now, we also know that minimum value of sine function is -1

So, minimum value of sin(2a)/2 is -1/2

Therefore, minimum value of
sin(a) sin(b) is -1/2


【 Hope it helps you 】

Answer 2

HEY !!

GOOD EVENING ^_^

HERE IS YOUR ANSWER ==>>
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【 Let Alpha = a

And Beta = b 】
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It's given that : a+b = 90°

=> a = 90° - b

So,

Sin (a) Sin (b) = Sin (90° - b) Sin (b)

=> Cos (b) Sin (b) ....... Equation [1]

We know that : Sin (Theta) = 2Sin (Theta) × Cos (Theta),

On Dividing both side by 2 ,

Sin (2b) / 2 = Sin (b) × cos (b) ..... Equation (2)

So, from (1) & (2)

Sin (a) Sin (b) = Sin (2a) / 2

Sin function has maximum value as 1

So, maximum value of Sin (2a) / 2 is 1/2

=>【【 Therefore, maximum value of
Sin (a) Sin (b) is 1/2. 】】
______

We also know that Sin function has minimum value as -1

So, minimum value of Sin (2a) / 2 is -1/2

=> 【【 Therefore, minimum value of
Sin (a) Sin (b) is -1/2. 】】
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Hope it works out ☺️

Have a Great day Ahead :-)

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