Question

If sin (x-20)°= cos (3x - 10°, then find the value of x. ​

Answer 1

Answer:

Step-by-step explanation:

Hi ,

This is related to Trigonometric Ratios of Complementary Angles.

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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

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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