Is 1-sin^2(-θ)=cos^2(θ) ?

The answer to whether 1-sin^2(-θ)=cos^2(θ) is True

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prove 1-sin^2(-θ)=cos^2(θ)

prove

1 - sin^{2} (- θ) = cos^{2} (θ)

True

Solution steps

1 - sin^{2} (- θ) = cos^{2} (θ)

Manipulating left side

1 - sin^{2} (- θ)

Use the negative angle identity:

sin (- x) = - sin (x)

= 1 - (- sin (θ))^{2}

Simplify

= 1 - sin^{2} (θ)

Rewrite using trig identities

1 - sin^{2} (θ)

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

1 - sin^{2} (x) = cos^{2} (x)

= cos^{2} (θ)

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) csc^{2} (θ) - tan (θ) = cot (θ)

\frac{1 + sec ( θ )}{csc ( θ )} - tan (θ) = sin (θ)

\frac{1 + cot ( x )}{1 + tan ( x )} = cot (x)

cos (α + β) + cos (α - β) = 2 cos (α) cos (β)

\frac{1 - cos ^{2} ( x )}{cos ^{2} ( x )} = tan^{2} (x)