Question

prove tan²A + cot²A + 2 = sec²A x cosec²A​

Answer 1

Step-by-step explanation:

L.H.S=tan²A+cot²A+1+1

=(tan²A+1)+(cot²A+1)(since, 1+tan²A=sec²A and 1+cot²A=cosec²A)

=sec²A+cosec²A

=(1/cos²A)+(1/sin²A)

taking l.c.m

= (sin²A+cos²A)/sin²A*cos²A

=1/sin²A*cos²A (since, sin²A+ cos²A =1)

=sec²A*cosec²A