Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

sin⁡2(10)−sin⁡2(70)−sin⁡2(20)+sin⁡2(80)\sin^2(10) - \sin^2(70) - \sin^2(20) + \sin^2(80)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Multiply radical expressionsright chevron icon

Full solution

Q. sin⁡2(10)−sin⁡2(70)−sin⁡2(20)+sin⁡2(80)\sin^2(10) - \sin^2(70) - \sin^2(20) + \sin^2(80)
  1. Rewrite using identity: Use the identity sin⁡2(θ)=1−cos⁡(2θ)2\sin^2(\theta) = \frac{1 - \cos(2\theta)}{2} to rewrite each term.\newlinesin⁡2(10)=1−cos⁡(20)2\sin^2(10) = \frac{1 - \cos(20)}{2}\newlinesin⁡2(70)=1−cos⁡(140)2\sin^2(70) = \frac{1 - \cos(140)}{2}\newlinesin⁡2(20)=1−cos⁡(40)2\sin^2(20) = \frac{1 - \cos(40)}{2}\newlinesin⁡2(80)=1−cos⁡(160)2\sin^2(80) = \frac{1 - \cos(160)}{2}
  2. Substitute into equation: Substitute the expressions back into the original equation.\newline(1−cos⁡(20))/2−(1−cos⁡(140))/2−(1−cos⁡(40))/2+(1−cos⁡(160))/2(1 - \cos(20))/2 - (1 - \cos(140))/2 - (1 - \cos(40))/2 + (1 - \cos(160))/2
  3. Combine like terms: Combine like terms.\newline(12−12−12+12)−(cos⁡(20)/2−cos⁡(140)/2−cos⁡(40)/2+cos⁡(160)/2)(\frac{1}{2} - \frac{1}{2} - \frac{1}{2} + \frac{1}{2}) - (\cos(20)/2 - \cos(140)/2 - \cos(40)/2 + \cos(160)/2)
  4. Simplify constants and cosine terms: Simplify the constant terms and combine the cosine terms. \newline0−(cos⁡(20)/2−cos⁡(140)/2−cos⁡(40)/2+cos⁡(160)/2)0 - (\cos(20)/2 - \cos(140)/2 - \cos(40)/2 + \cos(160)/2)
  5. Use cosine angle sum identities: Use the cosine angle sum identities, cos⁡(180−θ)=−cos⁡(θ)\cos(180 - \theta) = -\cos(\theta) and cos⁡(θ)=cos⁡(−θ)\cos(\theta) = \cos(-\theta), to rewrite cos⁡(140)\cos(140) and cos⁡(160)\cos(160).\newline−cos⁡(20)/2+cos⁡(40)/2−cos⁡(20)/2-\cos(20)/2 + \cos(40)/2 - \cos(20)/2
  6. Combine cosine terms: Combine the cosine terms. −cos⁡(20)/2−cos⁡(20)/2+cos⁡(40)/2-\cos(20)/2 - \cos(20)/2 + \cos(40)/2
  7. Final simplification: Simplify the expression. −cos⁡(20)+cos⁡(40)2-\cos(20) + \frac{\cos(40)}{2}

More problems from Multiply radical expressions

Question
Find the real-number root. \newline16\sqrt{16}\newline\newlineWrite your answer in simplified form. \newline____\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the real-number root. \newline916\sqrt{\frac{9}{16}}\newlineSimplify your answer and write it as a decimal or as a proper or improper fraction.\newline_____\_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the real-number root using a calculator. Round your answer to the nearest thousandth. \newline`\sqrt{957} `\newline _______
Get tutor helpright-arrow

Posted 2 months ago

Question
Multiply. Write your answer in simplest form. \newline273×42\sqrt{273} \times \sqrt{42}\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Simplify. \newline634\sqrt{\frac{63}{4}}\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify. Rationalize the denominator.\newline−49−2\frac{-4}{9 - \sqrt{2}}\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for z z .\newline16=z 16 = \sqrt{z} \newlinez= z = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify the radical expression. 14x14 \sqrt{14x^{14}} Write your answer in the form A A , B \sqrt{B} , or AB A\sqrt{B} , where A A and B B are constants or expressions in x x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A A . ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify the radical expression.\newline12x12\sqrt{12x^{12}}\newlineWrite your answer in the form AA, B\sqrt{B}, or ABA\sqrt{B}, where AA and BB are constants or expressions in xx. Use at most one radical in your answer, and at most one absolute value symbol in your expression for AA.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the value of sin⁡(5π6)? \sin \left(\frac{5 \pi}{6}\right) ? \newlineChoose 11 answer:\newline(A) −32 -\frac{\sqrt{3}}{2} \newline(B) −22 -\frac{\sqrt{2}}{2} \newline(C) 12 \frac{1}{2} \newline(D) 150150
Get tutor helpright-arrow

Posted 4 months ago

View all (18)