sin (A + B) = sin A cos B + cos A sin B
sin (A - B) = sin A cos B - cos A sin B
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
Problems 1-4 : Use the trigonometric ratio table given below to evaluate the given trigonometric ratio.
Problem 1 :
cos 15°
Solution :
= cos 15°
= cos (45° - 30°)
Use the identity of cos (A - B).
= cos 45° cos 30° + sin 45° sin 30°
Substitute the values for the trigonometric ratios from the table above.
Problem 2 :
cos 105°
Solution :
= cos 105°
= cos (60° + 45°)
Use the identity of cos (A + B).
= cos 60° cos 45° - sin 60° sin 45°
Substitute the values for the trigonometric ratios from the table above.
Problem 3 :
sin 75°
Solution :
= sin 75°
= sin (45° + 30°)
Use the identity of sin (A + B).
= sin 45° cos 30° + cos 45° sin 30°
Substitute the values for the trigonometric ratios from the table above.
Problem 4 :
tan 15°
Solution :
= tan 15°
= tan (45° - 30°)
Use the identity of tan (A - B).
Problem 5 :
If A and B are acute angles, find cos (A + B).
Solution :
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Since A and B are acute angles, they lie in Ist quadrant. In Ist quadrant, all trigonometric ratios are psitive.
So,
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Evaluating cos (A + B) :
= cos (A + B)
= cos A cos B - sin A sin B
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