Question

if cot B = 12/5 , prove that tan² B - sin²B = sin⁴ B sec² B​

Answer 1

Step-by-step explanation:

tanB=5/12

hypotenuse=√12^2+5^2=√169=13

sinB=5/13. cosB=12/13

tan^2B-sin^2B=25/144 -25/169

=25(169-144)/144*169

=25*25/144*169

multiply and divide by 169

=25*25*169/144*169*169

=(25*25/169*169)*(169/144)

=(5/13)^4*(13/12)^2

=sin^4B*sec^2B