tan1*tan2*tan3*.........tan89*=1

Asked by singhtaran652 | 7th Jan, 2019, 06:31: PM

Expert Answer:

begin mathsize 18px style tan space 1 space cross times space tan space 2 space cross times....... cross times tan space 88 space cross times tan space 89
equals tan space 1 space cross times space tan space 2 space cross times....... cross times tan space open parentheses 90 minus 2 close parentheses space cross times tan space open parentheses 90 minus 1 close parentheses
equals tan space 1 space cross times space tan space 2 space cross times....... cross times cot space 1 space cross times space cot space 2
equals tan space 1 space cross times cot space 1 cross times space tan space 2 space cross times cot space 2 cross times.........
equals fraction numerator tan space 1 over denominator tan space 1 end fraction cross times fraction numerator tan space 2 over denominator tan space 2 end fraction cross times.....
equals 1 end style

Answered by Arun | 8th Jan, 2019, 10:15: AM