Evaluate the following:(i) sin 78° cos 18° – cos 78° sin 18°�

1.	Evaluate the following:(i) sin 78° cos 18° – cos 78° sin 18° (ii) cos 47° cos 13° – sin 47° sin 13°(iii) sin 36° cos 9° + cos 36° sin 9° (iv) cos 80° cos 20° + sin 80° sin 20°
Answer» (i) As we know that sin (A – B) = sin A cos B – cos A sin B sin 78^° cos 18^° – cos 78^° sin 18^° = sin(78 – 18)° = sin 60° = √3/2 (ii) As we know that cos A cos B – sin A sin B = cos (A + B) cos 47^° cos 13^° – sin 47^° sin 13^° = cos (47 + 13)° = cos 60° = 1/2 (iii) As we know that sin (A + B) = sin A cos B + cos A sin B sin 36^° cos 9^° + cos 36^° sin 9^° = sin (36 + 9)° = sin 45° = 1/√2 (iv) As we know that cos A cos B + sin A sin B = cos (A – B) cos 80^° cos 20^° + sin 80^° sin 20^° = cos (80 – 20)° = cos 60° = 1/2

Evaluate the following:(i) sin 78° cos 18° – cos 78° sin 18° (ii) cos 47° cos 13° – sin 47° sin 13°(iii) sin 36° cos 9° + cos 36° sin 9° (iv) cos 80° cos 20° + sin 80° sin 20°

Answer»

(i) As we know that sin (A – B) = sin A cos B – cos A sin B

sin 78^° cos 18^° – cos 78^° sin 18^° = sin(78 – 18)°

= sin 60°

= √3/2

(ii) As we know that cos A cos B – sin A sin B = cos (A + B)

cos 47^° cos 13^° – sin 47^° sin 13^° = cos (47 + 13)°

= cos 60°

= 1/2

(iii) As we know that sin (A + B) = sin A cos B + cos A sin B

sin 36^° cos 9^° + cos 36^° sin 9^° = sin (36 + 9)°

= sin 45°

= 1/√2

(iv) As we know that cos A cos B + sin A sin B = cos (A – B)

cos 80^° cos 20^° + sin 80^° sin 20^° = cos (80 – 20)°

= cos 60°

= 1/2