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Question
Prove the following:
sec 840° . cot (– 945°) + sin 600° tan (– 690°) = `3/2`
Solution
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° + 45°)
= – cot 45°
= – 1
sin 600° = sin (360° + 240°)
= sin (240°)
= sin (180° + 60°)
= – sin 60°
= `-sqrt(3)/2`
tan (– 690°) = – tan 690°
= – tan (360° + 330°)
= – tan (330°)
= – tan (360° – 30°)
= – (– tan – 30°)
= tan 30°
= `1/sqrt(3)`
L.H.S. = sec 840° cot (– 945°) + sin 600° tan (– 690°)
= `(-2) (-1) + (-sqrt(3)/2)(1/sqrt(3))`
= `2 - 1/2`
= `3/2`
= R.H.S.
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