Angles α and β are the two acute angles in a right triangle. use the relationship between sine and cosine to find the value of β if β < α. sin( x/2 + 2x) = cos(2x + 3x/2 )

a) 15°

b) 37.5°

c) 52.5°

d) 75°

From given relation the value of β is 37.5°

Step-by-step explanation:

Given as :

α and β are two acute angles of right triangle

Acute angle have measure less than 90°

Now given as :

=

Or, =  

SO, =

Or, 90° =   +

or, 90° = + 4x

Or,  90° =  

So, x =   = 15°

∴ =

So, = sin

∴  The value of Ф_1 = = 37.5°

Similarly   =  

So ,The value of Ф_2 = = 52.5°

∵ β   α

So, As 37.5°52.5°

∴ β = 37.5°

Hence From given relation the value of β is 37.5°  Answer

the answer is b