0

Guest

Courses New

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?

 
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?

Grade:12

1 Answers

Arun
25750 Points
5 years ago
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

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More