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Grade: 12
        
 
tan 40 * tan 80* tan 20=(sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20
 now, multiplying numerator and denominator by 2,
                                 =(2*sin 40*sin 80) *sin 20 /(2 cos 40*cos 80) cos 20]
                                 =(cos 40- cos 120)*sin 20/( (cos 120+ cos 40) cos 20
                                 =(2 cos 40 +1) sin 20 /(2 cos 40-1) cos 20
                                 =(2 cos 40*sin 20 +sin 20) /(2 cos 40 cos 20 -cos 20)
                                 =(sin 60 -sin 20 +sin 20)/ (cos 60+sin 20-sin 20)
                                = sin 60/cos 60
                                 =tan 60
***how can the third lines come?
10 months ago

Answers : (1)

Arun
21467 Points
							
Dear student
 
use 
2sin a sinb = cos (a – b)  – cos (a+b)
 
and 2 cos a cosb = cos (a+b) + cos (a – b)
 
Regards
Arun
10 months ago
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