Question

Prove that (cosec a-sin a)(sec a-cos a)(tan a+cot a)=1

Answer 1

Given:(cosec a-sin a)(sec a-cos a)(tan a-cot a)=1.

consider,LHS

>> (1/sin a - sin a)(1/cos a- cos a)(sin a/cos a+cos a /sin a)

>>(1-sin^2 a/sin a)(1-cos^2 a/cos a)(sin^2 a+cos^2 a)

>>(cos^2 a/sin a)(sin^ 2 a/cos a)(1/cos a.sin a)

after cancellation we get LHS =1.

Hence,(cosec a-sin a)(sec a-cos a)(tan a+cot a)=1