Without using trigonometric tables, prove that: (i) \( \sin 32^{\circ} \cos 58^{\circ}+\cos 32^{...
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0Without using trigonometric tables, prove that:
(i) \( \sin 32^{\circ} \cos 58^{\circ}+\cos 32^{\circ} \sin 58^{\circ}=1 \)
(ii) \( \cos 54^{\circ} \cos 36^{\circ}-\sin 54^{\circ} \sin 36^{\circ}=0 \)
(iii) \( \sec 70^{\circ} \sin 20^{\circ}+\cos 20^{\circ} \operatorname{cosec} 70^{\circ}=2 \)
(iv) \( \tan 15^{\circ} \tan 60^{\circ} \tan 75^{\circ}=\sqrt{3} \)
(v) \( \tan 48^{\circ} \tan 23^{\circ} \tan 42^{\circ} \tan 67^{\circ} \tan 45^{\circ}=1 \)
(vi) \( \left(\sin 72^{\circ}+\cos 18^{\circ}\right)\left(\sin 72^{\circ}-\cos 18^{\circ}\right)=0 \)
(vii) \( \operatorname{cosec} 39^{\circ} \cos 51^{\circ}+\tan 21^{\circ} \cot 69^{\circ}-\sec ^{2} 21^{\circ}=0 \)
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