Question

Cos²105-sin²105.............​

Answer 1

cos(2·105⁰)=cos210⁰=cos(180⁰+30⁰)=-cos30⁰=-√3/2

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Answer 2

The expression you've given involves trigonometric identities. To simplify it, you can use the double-angle identity for sine and cosine:

cos(2θ) = cos²(θ) - sin²(θ)

In your expression, θ is 105 degrees. So, you can rewrite the expression as follows:

cos²(105) - sin²(105) = cos(2 * 105)

Now, let's calculate cos(2 * 105):

cos(2 * 105) = cos(210)

To simplify further, you can use the fact that the cosine function is periodic with a period of 360 degrees:

cos(210) = cos(210 - 360)

Now, find the cosine of -150 degrees:

cos(-150) = cos(150)

You can use the trigonometric identity that relates the cosine of an angle to the cosine of its supplementary angle:

cos(150) = -cos(30)

Now, you can use the value of cos(30) which is √3/2:

cos(150) = -√3/2

So, the simplified value of the expression cos²(105) - sin²(105) is:

-√3/2