Question

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

step by step solution required

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Answer 1

The minimum values of sin alpha and sin beta are (-1/2) and (1/2).


Hope this helps!

Answer 2

Answer:

Maximum and minimum value of sinα sinβ is 1/2 and -1/2  respectively.

Step-by-step explanation:

Given: $\alpha+\beta=90^{\circ}=\frac{\pi}{2}$

To find: Maximum and Minimum Value of $sin\,\alpha\:\,sin\,\beta$

Consider,

$sin\,\alpha\:\,sin\,\beta$

$=sin\,\alpha\:\,sin\,(\frac{\pi}{2}-\aplha)$

Using Complementary angle rule,

$=sin\,\alpha\:\,cos\,\alpha$

$=\frac{2}{2}\times sin\,\alpha\:\,cos\,\alpha$

$=\frac{2sin\,\alpha\:\,cos\,\alpha}{2}$

Using Half Angle formula of trigonometry,

$=\frac{sin\,2\alpha}{2}$

Range of the sin function is [ -1 , 1 ]

⇒ Maximum Value = 1

⇒ Minimum Value = 1

So, Maximum Value of sinα sinβ = $\frac{1}{2}$

Minimum Value of sinα sinβ = $\frac{-1}{2}$

Therefore, Maximum and minimum value of sinα sinβ is 1/2 and -1/2  respectively.