Question

(1 - tan A ) square + (1 - cot A ) square = ( sec A - cosec A ) square .​

Answer 1

Step-by-step explanation:

(1-tanA)²+(1-cotA)²

=(1-2tanA+tan²A)+(1-2cotA+cot²A)

=2-2(tanA+cotA)+(sec²A-1)+(cosec²A-1)

=-2(1/sinAcosA)+sec²A+cosec²A

=-2secAcosecA+sec²A+cosec²A

=sec²A-2secAcosecA+cosec²A

=(secA-cosecA)²