Show that

(I) tan 48° tan 23° tan 42° tan 67° = 1

(II)cos 38° cos 52° − sin 38° sin 52° = 0

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Solution

(I) tan 48° tan 23° tan 42° tan 67°

= tan (90° − 42°) tan (90° − 67°) tan 42° tan 67°

= cot 42° cot 67° tan 42° tan 67°

= (cot 42° tan 42°) (cot 67° tan 67°)

= (1) (1)

= 1

(II) cos 38° cos 52° − sin 38° sin 52°

= cos (90° − 52°) cos (90°−38°) − sin 38° sin 52°

= sin 52° sin 38° − sin 38° sin 52°

= 0

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Fill in the blanks:
i) $t a n 48^{\circ} . t a n 23^{\circ} . t a n 42^{\circ} . t a n 67^{\circ}$ = ___
ii) $c o s 38^{\circ} . c o s 52^{\circ} - s i n 38^{\circ} . s i n 52^{\circ}$ = ___

Q. Show that:

c o s 38^{\circ} c o s 52^{\circ} - s i n 38^{\circ} s i n 52^{\circ} = 0

Q. show that

cos 38^{\circ} cos 52^{\circ} - sin 38^{\circ} sin 52^{\circ} = 0

Q. Question 2 (ii)
Show that :

c o s 38^{\circ} c o s 52^{\circ} - s i n 38^{\circ} s i n 52^{\circ} = 0

Q. Show that

t a n 48^{0} t a n 23^{0} t a n 42^{0} t a n 67^{0} - 1

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Show that (I) tan 48° tan 23° tan 42° tan 67° = 1 (II)cos 38° cos 52° − sin 38° sin 52° = 0

Show that

(I) tan 48° tan 23° tan 42° tan 67° = 1

(II)cos 38° cos 52° − sin 38° sin 52° = 0