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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

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

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

cos (2 x) - (cos (2 x) - 1)

- (cos (2 x) - 1) : - cos (2 x) + 1

- (cos (2 x) - 1)

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - cos (2 x) + 1

= cos (2 x) - cos (2 x) + 1

Add similar elements:

cos (2 x) - cos (2 x) = 0

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

2 cot (4 x) = cot (2 x) - tan (2 x)

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

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

\frac{tan ^{2} ( x )}{1 + tan ^{2} ( x )} = sin^{2} (x)

\frac{sin ( x )}{cos ( x )} = tan (x)