Is cos^2(B)-sin^2(B)=1-2sin^2(B) ?

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

Popular >

prove cos^2(B)-sin^2(B)=1-2sin^2(B)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (B) - sin^{2} (B)

Rewrite using trig identities

cos^{2} (B) - sin^{2} (B)

Use the Pythagorean identity:

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

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

= 1 - sin^{2} (B) - sin^{2} (B)

Add similar elements:

- sin^{2} (B) - sin^{2} (B) = - 2 sin^{2} (B)

= 1 - 2 sin^{2} (B)

= 1 - 2 sin^{2} (B)

We showed that the two sides could take the same form

\Rightarrow True

cot (x) cos (2 x) = - sin (2 x) + cot (x)

cot (u) tan (u) - cos^{2} (u) = sin^{2} (u)

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )} = csc^{2} (x) + 1

sin (2 x) tan (x) = 1 - cos (2 x)

\frac{1}{csc ( x )} = sin (x)

Is cos^2(B)-sin^2(B)=1-2sin^2(B) ?
The answer to whether cos^2(B)-sin^2(B)=1-2sin^2(B) is True