Question

if sec teta +tan teta=3 then sin teta =

Answer 1

Step-by-step explanation:

Given,

sec∅ + tan∅ = 3 → (1)

W.K.T,

_______________

sec²∅ - tan²∅ = 1

_______________

(sec∅+tan∅)(sec∅-tan∅) = 1

[Since (a²-b²) = (a+b)(a-b)]

(3)(sec∅ - tan∅) = 1

sec∅ - tan∅ = ⅓ → (2)

By solving equation (1)&(2),

sec∅ + tan∅ = 3

sec∅ - tan∅ = ⅓

_____________

2sec∅ = 3+⅓

2sec∅ = (9+1)/3

2sec∅ = 10/3

sec∅ = (10/3)/(2)

sec∅ = 10/3 × ½

:. sec∅ = 5/3

Substitute 'sec∅' value in equation (1),

sec∅ + tan∅ = 3

5/3 + tan∅ = 3

tan∅ = 3 - 5/3

tan∅ = (9-5)/3

:. tan∅ = 4/3

tan∅ = sin∅/cos∅

sin∅/cos∅ = 4/3

sin∅.(1/cos∅) = 4/3

sin∅.sec∅ = 4/3

sin∅.(5/3) = 4/3

sin∅ = (4/3)/(5/3)

sin∅ = 4/3 × 3/5

:. sin∅ = 4/5.

I hope it hels you!!!