Question

if sec theta plus tan theta is =4. find sin theta and cos theta​

Answer 1

Answer

sin theta = 15/17, cos theta= 8/17

Step-by-step explanation:

sec theta+tan theta =4

[1/(cos theta)]+[sin theta/cos theta] =4

(1+sin theta)/cos theta =4

1+sin theta =4 cos theta

Squaring on both sides,

1+sin^2 theta+ 2 sin theta= 16 cos^2 theta

= 16-16 sin^2 theta

17 sin^2 theta+2 sin theta-15= 0

Let sin theta be 'x'

17x^2+2x-15= 0

17x^2+17x-15x-15= 0

17x(x+1) -15(x+1)= 0

(x+1)(17x-15)= 0

x= -1 or x= 15/17; when sin theta= -1, cos theta=0

hence, tan theta is infinity

sin theta= 15/17, cos theta= root(1-sin^2 theta)= 8/17