(Q1)Are these identities true only for 0° ≤ A ≤ 90°? If not, for which other values of A they are true?

i. sec²A - tan²A = 1

Given identity is sec2 A – tan2 A = 1

Let A = 0°

L.H.S. = sec2 0° – tan2 0°

= – 0 = = R.H.S.

Let A = 90°

tan A and sec A are not defined.

So it is .

∴ For all given values of ‘A’ such that 0° ≤ A ≤ 90° this trigonometric identity is .

ii. cosec²A - cot² A = 1

Given identity is cosec2 A – cot2 A = 1

Let A = 0°

cosec A and cot A are not defined for A = 0°.

Therefore identity is true for A = 0°.

Let A = 90°

cosec A = cosec ° =

cot A = cot ° =

L.H.S. = 2 – 2 = – = = R.H.S.

∴ This identity is true for all values of A, such that 0° ≤ A ≤ 90°.