Question

secA-1=(√2-1)tanA solve it​

Answer 1

Answer:

sec A - 1 = (√2 - 1) tan A

=> (sec A - 1)/tan A = (√2 - 1)

=> (sec A/tan A) - (1/tan A) = (√2 - 1)

=> cosec A - cot A = (√2 - 1) --------- (1)

=> *1/(cosec A + cot A) = (√2 - 1) (See 'Note' below)

=> cosec A + cot A = 1/(√2 - 1) = (√2 + 1) ------ (2)

Subtracting (1) from (2), we have : 2 cot A = 2

=> cot A = 1

=> tan A = 1 = tan (π/4)

=> A = nπ + (π/4) [n = 0, 1, 2, 3, ---------]

* Note : cosec A - cot A = (cosec A - cot A)/1

= (cosec A - cot A)/(cosec² A - cot² A)

= 1/(cosec A + cot A