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Grade: 12

                        

Show that: tan 48° tan 23° tan 42° tan 67° = 1 jsshudhwuhujwnijsdiw

one month ago

Answers : (1)

Anand Kumar Pandey
askIITians Faculty
1452 Points
							Dear Student

tan 48° tan 23° tan 42° tan 67°
Simplify the given problem
by converting some of the tan functions to the cot functions
We know that,
tan 48° = tan (90° - 42°)
= cot 42°
tan 23° = tan (90° - 67°)
= cot 67°

= tan (90° - 42°) tan (90° - 67°) tan 42° tan 67°
Substitute the values
= cot 42° cot 67° tan 42° tan 67°
= (cot 42° tan 42°) (cot 67° tan 67°)
= 1×1
= 1

Thanks
one month ago
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