Question

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Answer 1

Ответ:

Пошаговое объяснение:

1) cosx-(1-cos^2x)=1. 2)cosx+cosx=1. 3)2cosx=1. 4) cosx=1/2. t= +- (плюс минус ) п/3 +2пн

Answer 2

It looks like you've provided a series of characters followed by an equation: "cos x - sin^2x = 1." It seems you might be asking for a solution to this trigonometric equation.

To solve the equation, we can use trigonometric identities and algebraic manipulations. First, let's manipulate the equation:

cos x - sin^2x = 1

Since sin^2x = 1 - cos^2x (using the Pythagorean identity: sin^2x + cos^2x = 1), we can substitute it into the equation:

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

Now, let's simplify:

cos x - 1 + cos^2x = 1

Next, let's move all terms to one side of the equation:

cos^2x + cos x - 2 = 0

Now, we have a quadratic equation in terms of cos x. To solve for cos x, we can factor the quadratic equation or use the quadratic formula:

cos^2x + cos x - 2 = 0

Factoring:

(cos x - 1)(cos x + 2) = 0

Setting each factor to zero:

cos x - 1 = 0 or cos x + 2 = 0

Solving for cos x:

1. cos x = 1
2. cos x = -2

However, the cosine function's range is -1 to 1, so the second solution (cos x = -2) is not valid.

Therefore, the solution to the equation cos x - sin^2x = 1 is cos x = 1.

Keep in mind that trigonometric equations can have multiple solutions within a given range (usually 0 to 2π or 0 to 360 degrees). If you need specific solutions in a particular range, please let me know.