Question -
Answer -
(i) sin 780 cos 180 –cos 780 sin 180
We know that sin (A – B) = sin A cos B – cos A sin B
sin 780 cos 180 – cos780 sin 180 = sin(78 – 18) °
= sin 60°
= √3/2
(ii) cos 470 cos 130 –sin 470 sin 130
We know that cos A cos B – sin A sin B = cos (A + B)
cos 470 cos 130 – sin470 sin 130 = cos (47 + 13) °
= cos 60°
= 1/2
(iii) sin 360 cos 90 +cos 360 sin 90
We know that sin (A +B) = sin A cos B + cos A sin B
sin 360 cos 90 + cos360 sin 90 = sin (36 + 9) °
= sin 45°
= 1/√2
(iv) cos 800 cos 200 +sin 800 sin 200
We know that cos A cos B + sin A sin B = cos (A – B)
cos 800 cos 200 + sin800 sin 200 = cos (80 – 20) °
= cos 60°
= ½