Question

A simplified version of sin2 θ (1 + cot2 θ) = 1 is

Answer 1

sin2 θ (1 - tan2 θ) = 1

Answer 2

Do you remember the trig rules?

Answer 3

sin2x (1 + cot2x) = 1?

Answer 4

Using the rules
\[\sin(2x)(1+\frac{\cos(2x)}{\sin(2x)})=1 \\ \\ \sin(2x)+\cos(2x)=1 \\ \\ \text{Simplify \it further by using }Rsin(\theta +x), \]

Answer 5

Do you get it?

Answer 6

Here, you should use \[Rsin(2 \theta +2x)\]
\[\sin(2x)+\cos(2x)=1 \\ \\ \text{When}~Rsin(2\theta+2x) , \text{Expanding it}\\ \\ Rsin(2 \theta)\cos(2x) + Rcos(2\theta)\sin(2x) \text{ Substituting this \to the equation,} \\ \\ \\ \sin(2x)(1-Rcos(2\theta))+\cos(2x)(1-Rsin(2 \theta) =1 \\ \\ \tan(2\theta)=1 \\ \\2 \theta=\frac{\pi}{4}\\ \\ R=\sqrt{1+1}\\ \\ R=\sqrt{2} \\ \\ \text{Moving back \to the original form,}{Rsin(2 \theta +2x)} \]
\[\sqrt{2} \sin \left(2 x+\frac{\pi }{4}\right)=1\]

Answer 7

I read it as Sin^2 and Cot^2 in which case, a simpler version is

1=1