Question

Sin^2(пи+@)+sin^2(пи\2+@) разделить на cos (3пи\2+@) умножить на ctg(3пи\2+@)

Answer 1

Числитель = Sin²(π+α) + Sin²(π/2 +α) = Sin²α + Cos²α = 1
знаменатель = Сos(3π/2 + α) = Sinα
теперь сам пример :
1/Sinα * Сtg(3π/2 + α) = - 1/Sinα * tgα = -1/Sinα*Sinα/Cosα = -1/Cosα

Answer 2

Let's break down the expression step by step:

1. Simplify the trigonometric expressions:

   $\sin^2(\pi + @)$ can be simplified using the angle sum identity $\sin(\alpha + \beta) = \sin\alpha\cos\beta + \cos\alpha\sin\beta$:

   $\sin^2(\pi + @) = \sin^2\pi\cos^2@ + \cos^2\pi\sin^2@ = \sin^2@.$

   Similarly, $\sin^2(\frac{\pi}{2} + @)$ can be simplified using the angle sum identity $\sin\left(\frac{\pi}{2} + \beta\right) = \cos\beta$:

   $\sin^2\left(\frac{\pi}{2} + @\right) = \cos^2@.$

   Now, we have the expression:

   $\sin^2@ + \cos^2@.$

2. Apply the Pythagorean identity:

   $\sin^2\theta + \cos^2\theta = 1.$

   So, the expression becomes $1.$

3. Simplify the denominator:

   Using the cosine tangent identity $\cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta},$ we have:

   $\cot\left(\frac{3\pi}{2} + @\right) = \frac{\cos\left(\frac{3\pi}{2} + @\right)}{\sin\left(\frac{3\pi}{2} + @\right)}.$

   The sine and cosine values for $\frac{3\pi}{2} + @$ are $-\cos@$ and $-\sin@$ respectively. Therefore,

   $\cot\left(\frac{3\pi}{2} + @\right) = \frac{-\cos@}{-\sin@} = \frac{\cos@}{\sin@}.$

4. Final expression:

   The original expression is $\frac{1}{\cot\left(\frac{3\pi}{2} + @\right)}.$

   Substituting the expression for $\cot\left(\frac{3\pi}{2} + @\right),$ we get:

   $\frac{1}{\frac{\cos@}{\sin@}} = \frac{\sin@}{\cos@}.$

So, the simplified expression is $\frac{\sin@}{\cos@}.$