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I need help with - Trigonometry - JEE Main-6

  1. If A, B, A – B and A + B are positive acute angles, find the values of A and B from

the equations sin (A – B) =\frac{1}{2}, cos (A + B) =\frac{1}{2}.

  • Option 1)

    A = 600 and B = 300

  • Option 2)

    A = 150 and B = 450.

  • Option 3)

    A = 450 and B = 150

  • Option 4)

    A = 300 and B = 300

 
Answers (1)
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As we learnt

 

Trigonometric Ratios of Special Angles -

 

- wherein

These are the values of trigonometric ratios for standard angles. 

 

 

The equations are sin (A – B) = \frac{1}{2} = sin 300 Þ A – B = 300.         …(1)

                        And cos (A + B) = \frac{1}{2} = cos 600 Þ A + B = 600.                          ...(2)

                        From (1) and (2), A = 450 and B = 150.


Option 1)

A = 600 and B = 300

Option 2)

A = 150 and B = 450.

Option 3)

A = 450 and B = 150

Option 4)

A = 300 and B = 300

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