Can you prove that sin^2(beta)(1+cot^2(beta))=1?

2 Answers
Apr 9, 2018

#LHS=sin^2(beta)(1+cot^2(beta))#

#=sin^2(beta)(1+cos^2(beta)/sin^2(beta))#

#=sin^2(beta)+sin^2(beta)*cos^2(beta)/sin^2(beta)#

#=sin^2(beta)+cos^2(beta)#

#=1=RHS#

Apr 9, 2018

See below.

Explanation:

#(sin^2(beta))(1+cot^2(beta))=1#

Identity:

#color(red)bb(cot(x)=cosx/sinx)#

Substituting in given equation:

#(sin^2(beta))(1+cos^2(beta)/sin^2(beta))=1#

Expanding:

#sin^2(beta)+sin^2(beta)cos^2(beta)/sin^2(beta)=1#

#sin^2(beta)+cancel(sin^2(beta))cos^2(beta)/cancel(sin^2(beta))=1#

#sin^2(beta)+cos^2(beta)=1#

This is the Pythagorean identity: