11th Math Important Questions For Exam 2026 🔥 | Most Expected Board Questions

Añadido: 2026-05-12

[00:00:00]We have brought an interesting question for you guys for the exam of first year mathematics. It is often repeated that when writing the term on expressions containing only cosin to the power of 1, we have to shift it to the power of cosin to one. Meaning cos should be to the power of one and it can be whatever it wants. Its second part is also important. I will give a hint about the second part also in the end.

[00:00:18]Right now let us solve this as to what will be its session? It's an easy scene. It is a very easy scene. Come to the solution.

[00:00:26]And when we come towards the solution, we put equal, sin is fine, the power of alpha and cospha will become 4, we took the power out, that means four and four together, like the roof fell, it fell on me, but when the roof goes up, it will go out from us two-three people, so the power went out, now the power is outside also. We get a formula 2sin θ cosθ is equal to sin 2θ. Keeping this formula in mind, I will simplify it a little. I will add it here inside the bracket, that is, inside it, and here 1 2 sin α cos α close to the power 4, that is, I added it by itself, multiplied it and also divided it. It will be cut to two and will again become a question. The formula will be closed here. The formula above 2sinha cosα will be closed sin 2α sin 2α bracket close of power 4 Now when the formula is closed then what will be the next step I have next step I have 1 to the power of 2α 4 separately sin of 2α to the power of 4 separately I have understood till here this is the next step not 1 8 2 4 1 16 1 16 means 2 * 2 * 2 * 2 so 2 * 2 = 4 4 * 2 = 18 8 * 2 = 16 square of sin²α is fine I separated the square on both sides square came here also square came here also and here there is 2α 2α 2 * 2 what will become 4 why did I do this I said I will share it with you guys that is Fula we have sin²α sin²α is equal to I have 1 - cos you guys have read this 2α / 2 basically Fula This is not it. The formula we have is sin² apha = square 1 - cos 2α/2 but we eliminated the square root. I put the square here and this square root is finished in the top one. So basically I will follow the above formula.

[00:02:34]When there is pay one here, there is pay two here. When this becomes sin² 2 alpha, what will happen here? 4 Alpha.

[00:02:45]What will happen here when it becomes 4? 8 Alpha When there will be 8 here, there will be repeated changes in the 16 flowers here. So what change will I get from here? What do I get in place of 1 16 bracket sin² 2 alpha? 1 - 1 - cos 4 / 2² Here we go. what shall we do now? We will open the formula on this. Only 16 is coming. Now let us take a minute and draw a line here.

[00:03:17]What will we do after here? 1 16 And then I'm going to have 1 - cos 4² / 4 because the square is open on the bottom one as well.

[00:03:28]Square got into this too. 1 16 * 4 1² 1 will become 1² 1. Plus cos² 4 cos² 4 - 2 cos 4α and 4 goes out so there's nothing left at the bottom. The forest will be saved. There is no need to write forest. Let's not write it in the next step. 116 * 4 16 * 4 1 64 and 1 minus write this down first. 2 cos 4 Let me write this down later because we still have to put flowers on it.

[00:04:07]As I have told you guys that sin sinha is equal to 1 - cos 2α / 2, similarly cosα = 1 + cos 2α / 2, here it is plus, there it is minus. Now after this it will be cos² which means it is also square. There is a square here too. Ok? No, it's not square here, so it's square root here, right? Sorry, write this square root cos² here now. What will happen if there are 2 alphas?

[00:04:40]1 + cos 4 / 2 cos of 4 alpha will be 1 + cos 8 / 2 Now I need the value of cos² and 4 alpha so this will be cos² 4 square root will be cut 1 + cos 8 alpha / 2 cos² instead of alpha this will come 1 64 1 - 2 cos 4 plus cos² and what will I get in place of 4 cos² and 4 alpha? 1 + cos 8 / 2 will be the LCM of all these. 1 64 will be the LCM of all these.

[00:05:22]Two this one will multiply by two this two will be - cos 4 + 1 a it is and cos of 8ha bracket close.

[00:05:35]After this, this too will go out. 64 * 2 = 128 1 2 + 1 3 - 4 cos 4 + cos 8 Alpha bracket shifted to close single power cosin.

[00:05:53]Shifted to single power cosine.

[00:05:55]Now I said that I will explain the second part to you a little bit. The second part is what do I have? sin 4α and cos square alpha is like that. What will you do now? Will you break it a little? If you write this as sin² alpha² and if you write this as cos alpha², what will come in place of cos alpha? cos² alpha. fixed bugs? Don't break it, of course.

[00:06:24]What will you get in place of cos² alpha?

[00:06:26]cos² alpha means sin, right? So cos² alpha will be replaced by 1 - 1 + cos 2α / 2, you can put this here. This will replace sin² alpha.

[00:06:39]This is 2α. Only sin² will replace alpha with this. You will put this formula here and then after this you will simplify both of them by multiplying them from above.

[00:06:50]Let me do one step.

[00:06:52]This will come in place of sin²α 1 - cos 2α / 2² here and 1 + cos 2α / 2 first there the formula will open above 1 - cos 2α² will become 4 below and 1 + cos 2α as it is divided / 2 will become 4 * 2 = 8 1² 1 + cos² 2α - 2 cos 2α bracket close 1 + cos 2α multiply the one above from the top, simplify etc. So that's the only question. fixed bugs? That 's the only question. I do Simplify. I hope you have understood. Let's go to point two