Question

tan²x/tan²x-1+cosec²x/sec²x-cosec²x=1/sin²x-cos²x​

Answer 1

Answer:

tan²x+cot²x=sec²x-1+csc²x-1=(csc²x+sec²x)-2

=>(csc²x+sec²x)-2+(csc²+sec²x)=2(csc²x+sec²x)-2=2(1/sin²x+1/cos²x)-2

=2{(sin²x+cos²x)/sin²x.cos²x}-2

=2/(sin²x.cos²x)-2

=2sec²x.csc²x-2

=>the value of expression becomes

=1+2sec²x.csc²x-2=2sec²x.csc²x-1=8/sin²2x-1

=>0<sin²2x<1=>0<8sin²2x<8=>0–1<8sin²2x-1<8–1

=>-1<the expression<7

=>It €(-1,7).Ans..