Question

Prove the following:

sec 840° cot (- 945°) + sin 600° tan (- 690°) = 3/2

Answer 1

sec 840° = sec (720° + 120°) 

= sec (2 x 360° + 120°)

= sec (120°) 

= sec (90° + 30°) 

= – cosec 30° 

= -2 

cot(-945°) = -cot 945° 

= -cot (720° + 225°) 

= -cot (2 x 360° +225°) 

= -cot (225°) 

= -cot (180° + 459) 

= -cot 45° 

= -1 

sin 600° = sin (360° + 240°) 

= sin (240°) 

= sin (180° +60°)

= – sin 60° = - √3/2

tan (-690°) = – tan 690° 

= – tan (360° +330°) 

= -tan (330°) 

=- tan (360° – 30°) 

=-(-tan 30°)

= tan 30°0 = 1/√3

L.H.S. = sec 840° cot (-945°) + sin 600° tan (-690°)

= (-2)(-1) + (- √3/2) (1/√3)

= 2 - 1/2 = 3/2

= R. H. S.