With topics like those, I continually convert each and each little element into words of sin and cos till eventually now I initiate fixing. For ease of writing, enable me replace all of your thetas with x'es. 3(tan^2 x - sec^2 x) 3((sin^2 x/cos^2 x) - (a million/cos^2 x)) 3((sin^2x - a million)/cos^2x) Now, do not ignore that sin^2 x + cos^2 x = a million. consequently, sin^2 x - a million = - cos^2 x So the equation turns into 3*(-a million) = -3. cos x * csc x / tan x (cos x * (a million/sin x)) / (sin x / cos x) (cos x / sin x) * (cos x / sin x) cos^2 x / sin^2 x = cot^2 x sin x * csc x / cot x sin x * (a million/sin x) / (cos x / sin x) a million / (cos x / sin x) sin x / cos x = tan x wish that helps!
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Verified answer
Sin = O / H
Cos = A / H
Tan = O / A
sec = H/O = 1/sin
csc = H/A = 1/cos
cot = 1/tan = A/O
Also,
tan = sin / cos
HINT: sin / tan = sin * cot
With topics like those, I continually convert each and each little element into words of sin and cos till eventually now I initiate fixing. For ease of writing, enable me replace all of your thetas with x'es. 3(tan^2 x - sec^2 x) 3((sin^2 x/cos^2 x) - (a million/cos^2 x)) 3((sin^2x - a million)/cos^2x) Now, do not ignore that sin^2 x + cos^2 x = a million. consequently, sin^2 x - a million = - cos^2 x So the equation turns into 3*(-a million) = -3. cos x * csc x / tan x (cos x * (a million/sin x)) / (sin x / cos x) (cos x / sin x) * (cos x / sin x) cos^2 x / sin^2 x = cot^2 x sin x * csc x / cot x sin x * (a million/sin x) / (cos x / sin x) a million / (cos x / sin x) sin x / cos x = tan x wish that helps!
sinθ/tanθ
Tangents is equal to sin/cos
sinθ/(sinθ/cosθ)
sinθcosθ/sinθ
Sinθ cancel e/o out and you're left with cosθ as your answer
sin^2/cos
(1 - cos^2)/cos
1/cos - cos
sec - cos
Sin(θ)/Tan(θ) =
Sin(θ)/(Sin(θ)/Cos(θ))
Sin(θ) * (Cos(θ)/Sin(θ))
The Sin(θ)s cancel out leaving only
Cos(θ)