Question

If sec θ + tan θ = 5, find the quadrant in which θ lies and find the value of sin θ.

Answer 1

Answer:

sinθ = 12/13

Step-by-step explanation:

Given:

 sec θ + tan θ = 5

(1/cos θ) + (sinθ /cos θ) = 5

(1+sinθ)/ cos θ = 5

Squaring on both sides

(1+sinθ )²/ cos²θ = 25

(1+sinθ )²/ 1 - sin²θ = 25

(1+sinθ )(1+sinθ ) / (1 - sinθ)(1+sinθ)=25

(1+sinθ ) / (1 - sinθ)=25

1+sinθ = 25(1-sinθ )

26 sinθ = 24

13 sinθ = 12

sinθ = 12/13

Answer 2

HELLO DEAR,




GIVEN:- sec θ + tan θ = 5


1/cosθ + sinθ/cosθ = 5

=> (1 + sinθ)/cosθ = 5

=> (1 + sinθ) = 5cosθ

[on squaring both side]

we get,

=> (1 + sinθ)²/cos²θ = 25

=> (1 + sinθ)(1 + sinθ)/(1 - sinθ)(1 + cosθ) = 25

=> (1 + sinθ)/(1 - sinθ) = 25

=> 1 + sinθ = 25 - 25sinθ

=> 26sinθ = 24

=> sinθ = 24/26 = 12/13



I HOPE IT'S HELP YOU DEAR,
THANKS