Is sin^2(x)+cos(2x)=1-sin^2(x) ?

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

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prove sin^2(x)+cos(2x)=1-sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

sin^{2} (x) + 1 - 2 sin^{2} (x) : - sin^{2} (x) + 1

sin^{2} (x) + 1 - 2 sin^{2} (x)

Group like terms

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

Add similar elements:

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

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

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

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

= 1 - sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (4 5^{\circ}) = \frac{sin ( 2 \cdot 4 5 ^{\circ} )}{2 \cdot sin ( 4 5 ^{\circ} )}

4 sin (3 x) cos (4 x) = 2 sin (7 x) - 2 sin (x)

sec^{2} (x) = \frac{sec ( x )}{cos ( x )}

cot (θ) \cdot sin (θ) = cos (θ)

2 sin^{2} (θ) + sin (θ) - 1 = 0

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