Question

sin^2 theta - cos^2 theta = 1

Answer 1

the identity is

\(\large\color{black}{ \rm sin^2 θ + cos^2θ = 1 }\)

Answer 2

\(\large\color{black}{ \bf sin^2 θ - cos^2θ = 1 }\)
\(\large\color{black}{ \bf sin^2 θ - (1-sin^2θ) = 1 }\)
\(\large\color{black}{ \bf sin^2 θ - 1+sin^2θ = 1 }\)
\(\large\color{black}{ \bf sin^2 θ+sin^2θ = 1+1 }\)
\(\large\color{black}{ \bf 2sin^2θ = 2 }\)
\(\large\color{black}{ \bf sin^2θ = 1 }\)
\(\large\color{black}{ \bf sinθ = ± 1 }\)

\(\large\color{black}{ \bf sin^{-1}1 =θ ~~~~~~and~~~~~~\large\color{black}{ \bf sin^{-1}1 =θ }}\)

Answer 3

I mean ^(-1)1, and ^(-1) -1

Answer 4

I like solomon's method :)
Another approach is to use the Cosine Double Angle Formula.
Just something else to try :D\[\Large\rm \cos^2x-\sin^2x=-1,\]\[\Large\rm \cos2x=-1,\]\[\Large\rm 2x=\pi+2k \pi,\]Solving for x gives,\[\Large\rm x=\frac{\pi}{2}+k \pi\]