how to verify csc(pi/2- θ)/cscθ=tan θ
Pi/2 is a fraction then the / sign is meant for dividing
SOME ONE SHOW ME HOW YOU DO IT PLEASE
π/2 radians = 90°
Are you familar with the the relationship between co-ratios?
that is,
e.g. sin 20° = cos 70°
cos 30 = = sin 60
sec 10 = csc 80
tan 50 = cot 30
etc
so csc(π/2-Ø) = sec Ø
LS = sec Ø/csc Ø
= (1/cosØ)/(1/sinØ)
= (1/cosØ)(sinØ/1)
=sinØ/cosØ
= tan Ø
To verify the equation csc(pi/2 - θ)/cscθ = tanθ, we can start by simplifying both sides of the equation separately:
1) Simplifying the left side:
csc(pi/2 - θ) represents the cosecant of (pi/2 - θ), which is equal to 1/sin(pi/2 - θ).
Using the trigonometric identity sin(pi/2 - θ) = cosθ, we can rewrite the left side of the equation as 1/cosθ.
2) Simplifying the right side:
tanθ represents the tangent of θ, which is equal to sinθ/cosθ.
We can rewrite the right side of the equation as sinθ/cosθ.
Now, we can compare the simplified left side (1/cosθ) with the simplified right side (sinθ/cosθ):
1/cosθ = sinθ/cosθ
Since both sides have a common denominator (cosθ), we can cancel it out, resulting in:
1 = sinθ
This is a true statement, as the sine of any angle θ is always between -1 and 1.
Therefore, we have verified that csc(pi/2 - θ)/cscθ = tanθ is true.