Question

If secA +tanA=3, secA-tanA=1/3 then find the value of:i) sinA ii) cotA +cosecA​

Answer 1

Since, sec(A) = 3 - tan(A)

Also, sec(A) = 1/3 + tan(A)

We can say, 3 - tan(A) = 1/3 + tan(A)

2 tan(A) = 3 - 1/3 = 8/3

tan(A) = 4/3

Clearly, sin(A) / cos(A) = 4 / 3

3 sin(A) = 4 cos(A)

Squaring both sides,

9 sin²(A) = 16 cos²(A) = 16 - 16 sin²(A)

25 sin²(A) = 16

sin(A) = 4/5

Hence, cos(A) = 3/5

cot(A) + cosec(A) = cos(A)/sin(A) + 1/sin(A) = (3/5) / (4/5) + 1 / (4/5)

cot(A) + cosec(A) = 3/4 + 5/4

cot(A) + cosec(A) = 2