Question

For what value of angle x does sin x = 4/3 exist ?

Answer 1

sinx = 4/3 = 1.333.. > 1

but we know that maximum value of sine is 1 so, sinx ≠ 4/3 it's not possible .

actually , sinx = p/h { p =>perpendicular , h => hypotenuse }

we know, h >P for all real value of P and h

so, P/h < 1

hence, sinx ≠ greater then 1

Answer 2

Answer:

=> {cosθ(1 + sinθ) + cosθ(1 - sinθ)}/(1 - sinθ)(1 + sinθ) = 4

=> {cosθ + cosθ.sinθ + cosθ - cosθ.sinθ}/(1 - sin²θ) = 4

=> 2cosθ/cos²θ = 4 [ we know, sin²x + cos²x = 1 so, (1 - sin²θ) = cos²θ]

=> 2/cosθ = 4

=> cosθ = 1/2 = cos60°

hence, in 0 < θ < 90° , θ = 60°

now, if given equation is not defined.

(1 - sinθ) = 0

in 0 < θ < 90° , sinθ = 1 at 90°

hence, equation is undefined at θ = 90°

[ note : one more case for undefined, (1 + sinθ) = 0 , but in 0 < θ < 90° it's not possible. thars why I didn't mention it above]

Step-by-step explanation: