Question

if tanA =1 ,then secA =?​

Answer 1

Answer:

Correct option is

C

cosA

We need to find value of (secA+tanA)(1−sinA)

Putting the values of secA and tanA as

secA=

cosA

1

tanA=

cosA

sinA

(

cosA

1

+

cosA

sinA

)(1−sinA)

=

cosA

1+sinA

(1−sinA)

,=

cosA

1−sin

2 A= cosA

cos

2 A .... (As 1−sin

2 A=cos

2 A)=cosA

Answer 2

Step-by-step explanation:

If sec A - tan A = 1/3, what is the value of sec A + tan A?

sec A - tan A = 1/3 (1)

sec A + tan A = m (2)

Add (1) and (2)

2 sec A = m + 1/3 = (3m+1)/3, or

sec A = (3m+1)/6

Subtract (1) from (2)

2 tan A = m - 1/3 = (3m-1)/3

tan A = (3m-1)/6 (4)

We know that 1 + tan^2 A = sec^2 A, or

1 + [(3m-1)/6]^2 = [(3m+1)/6]^2, or

1 + [9m^2 - 6m + 1]/36 = [9m^2 + 6m + 1]/36, or

36 + 9m^2 - 6m + 1 = 9m^2 + 6m + 1, or

36 - 6m = + 6m, or

12m = 36, or

m = 3

Hence sec A + tan A = 3.