This is the same as secant squared theta [sec²(Θ)].Take the identity sin²(Θ) + cos²(Θ) = 1Divide both sides by cos²(Θ):sin²(Θ) / cos²(Θ) = tan²(Θ)cos²(Θ) / cos²(Θ) = 11 / cos²(Θ) = sec²(Θ)tan²(Θ) + 1 = sec²(Θ)
Since there is no equation, there is nothing that can be solved.
The question contains an expression but not an equation. An expression cannot be solved.
It is 1.
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
If r-squared = theta then r = ±sqrt(theta)
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
To determine what negative sine squared plus cosine squared is equal to, start with the primary trigonometric identity, which is based on the pythagorean theorem...sin2(theta) + cos2(theta) = 1... and then solve for the question...cos2(theta) = 1 - sin2(theta)2 cos2(theta) = 1 - sin2(theta) + cos2(theta)2 cos2(theta) - 1 = - sin2(theta) + cos2(theta)
Cosine squared theta = 1 + Sine squared theta
This is the same as secant squared theta [sec²(Θ)].Take the identity sin²(Θ) + cos²(Θ) = 1Divide both sides by cos²(Θ):sin²(Θ) / cos²(Θ) = tan²(Θ)cos²(Θ) / cos²(Θ) = 11 / cos²(Θ) = sec²(Θ)tan²(Θ) + 1 = sec²(Θ)
Since there is no equation, there is nothing that can be solved.
The question contains an expression but not an equation. An expression cannot be solved.
Tan^2
cos2(theta) = 1 so cos(theta) = ±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
Your question is insufficiently precise, but I'll try to answer anyway. "Sine squared theta" usually means "the value of the sine of theta, quantity squared". "Sine theta squared" usually means "the value of the sine of the quantity theta*theta". The two are not at all the same.
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1
Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1