If sin x 20 cos 3x 10 find x
Asked by admin @ in Math viewed by 536 People
If sin[x-20]=cos[3x-10].find x
Answered by admin @
Hi ,
This is related to Trigonometric Ratios of Complementary Angles.
____________________________________________________________
As we know that two angles are said to be complementary if their
sum equals 90° .
i ) sin ( 90 - A ) = cos A
ii ) cos ( 90 - A ) = sin A
__________________________________________________________
According to the problem ,
a ) sin ( x - 20 ) = cos ( 3x - 10 )
⇒ sin ( x - 20 ) = sin [ 90 - ( 3x - 10 ) ]
⇒ x - 20 = [ 90 - ( 3x - 10 ) ]
⇒ x - 20 = 90 - 3x + 10
⇒ x + 3x = 90 + 10 + 20
⇒ 4x = 120
⇒ x = 120 / 4
∴ x = 30°
Or
sin ( x - 20 ) = cos ( 3x - 10 )
⇒ cos [ 90 - ( x - 20 ) ] = cos ( 3x - 10 )
⇒ 90 - ( x - 20 ) = 3x - 10
⇒ 90 - x + 20 = 3x - 10
⇒ 110 - x = 3x - 10
⇒ 110 + 10 = 3x + x
⇒ 120 = 4x
∴ 4x = 120
x = 120 / 4
x = 30°
I hope this helps you.
*****
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