Find cos |sin (-) - COS ~1(0)]. (Only basic mathematical operators, powers, and square roots are al- lowed in this answer box Trig functions are not allowed. For ex...

Find the exact value of $$\begin{aligned}\cos ^{2} 10^{\circ}+\cos ^{2} 20^{\circ}+\cos ^{2} 30^{\circ}+\cos ^{2} 40^{\circ}+\cos ^{2} 50^{\circ} \\+& \cos ^{2} 60^{\circ}+\cos ^{2} 70^{\circ}+\cos ^{2} 80^{\circ}\end{aligned}$$

Okay, so we need to use the formula for co sign of a plus B to find the exact value of coastline of 75 degrees. So we have that the co sign of a plus B is equal to the co sign of a the co sign of B minus. Sign of a sign of B. So let's do 75 as 45 plus 30. So this is the co sign of 45 tons, the coastline of 30 minus sign of 45 these air degrees sign of 30. So we know the coastline of 45 is the square root of two. Over to the coastline of 30 is the square root of three. Over to the sign of 45 is a squared of to over to, and the sign of 30 is one half. So we get that co sign of 75 degrees is equal to the square root of six minus the square root of two over four

We have to find out where you off course. Oh, sign in words. Squirrel. Tough to the white. Might do Bless because in Watts pretty you work by five Now, like el fa is equal toe sign in worse square root off to the one went to and pita is equal to Because in words three be worried by five No sign Alfa is equal toe swirled off to divide by two We can write it as cause fr he will do squared off one minus society where fr which is equal to the square root off to the wider by do similarly sign Vita is equal to squad went off what mine s got where beat up It is equal to 16 b y by 25 Always the bar untrue is equal to for the work by five No cause Mita is equal toe Could he be worried by fight Using the property God and far less pita is equal to los and far cost beat minus sign and far sign Beat up by using the formula weaken right swelled off to the world by two multiplied by three Wild by five minus squared off to we would like to when deployed. Why? For they weren't by five, which is equal to minus squared off to be won by that.

Problem number 77 in which we need to find the exact value off cause to cause in worst three by five course to cause inwards T by fight. Okay, so we need to use since this is two letters is on this to be X. So this becomes cost to works, which is equal to do, cause it's quite x minus one. So do, of course, cause inwards three by five squared minus one. Okay, so this will become three by five to into three by five square minus one. So two into fall by 25 minus one. This is 16/25 minus one, which is 16 minus 25 by 25. Bitch, you minus nine by 25. So the exact value is minus nine over 25. This is exactly

Hi, everyone. Today we're going to prove that the sign of 15 degrees is equal to the square root of tool minus square root of three inside that square over to using cosine of 30 being equal to 3/2. And we're gonna do this with a half angle formula. Sign of half theta is equal to square root of one minus cosine theta over to. And so to start off, we're going to treat our data as 30 degrees. Score half. That'll be 15. So the sign groups of 15 degrees, it's an equal square root of one minus and cosign theta. Here is Route 3/2. Mhm and all of this divided by two inside that square. And if we simplify this, we can split that fraction inside. So it becomes square root of half minus square root of 3/4. And now you ask how that becomes too minus or 3/2. Well, if we multiply the top and bottom of this fraction by two, well, we're going to get is the square root of two minus Route 3/4. And now we know that this was four on the bottom. Is 1/4 and the square root of one for this one half. So what we can do is pull that out of the square, root so to minus Route three and just leave a two on the bottom. Thanks for