n\frac{1}{\sin(x)},\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1} View solution steps. Steps for Solving Linear Equation. \frac { 1 } { n } = \sin ( x ) Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n. 1=n\sin(x) Solucionatus problemas matemáticos con nuestro solucionador matemático gratuito, que incluye soluciones paso a paso. Nuestro solucionador matemático admite matemáticas básicas, pre-álgebra, álgebra, trigonometría, cálculo y mucho más. sin(n + 1) x sin (n + 2) x + cos (n + 1) x cos (n + 2) x = cos ( ( n + 2 ) x − ( n − 1 ) x ) { ∵ cos ( A − B ) = sin A sin B + cos A cos B } ⇒ = cos ( ( n + 2 − n − 1 ) x ) DetailedSolution. Given if I n = ∫π −π sinnx (1+πx)sinx dx,(1) i f I n = ∫ − π π s i n n x ( 1 + π x) s i n x d x, ( 1) I n = ∫π −π πxsinnx (1+πx)sinx dx.(2) I n = ∫ − π π π x s i n n x ( 1 + π x) s i n x d x. ( 2) On adding Eqs. (i) and (ii), we have. Closed1 hour ago. Improve this question I am not able to do this sum the question is Prove that sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x So, kindly help me in doing this sum. Solution Verified by Toppr. The given equation is. sin −1x+sin −1(1−x)=cos −1x. ⇒sin −1x+sin −1(1−x)= 2π−sin −1x. ⇒sin −1(1−x)= 2π−2sin −1x (i) Let sin −1x=y. ⇒x=siny. wBtdhl. If $n$ is even, then $$1= \cos^{n}x-\sin^{n}x \leq 1-0=1$$ with equality if and only if $\cos^{n}x=1, \sin^nx=0$. If $n$ is odd, $$1= \cos^{n}x-\sin^{n}x \,,$$ implies $\cosx \geq 0$ and $\sinx <0$. Let $\cosx=y, \sinx=-z$, with $y,z \geq 0$. $$y^n+z^n=1$$ $$y^2+z^2=1$$ Case 1 $n=1$ Then , since $0 \leq y,z \leq 1$ we have $$1 =y+z \geq y^2+z^2 =1$$ with equality if and only if $y=y^2, z=z^2$. Case 2 $n \geq 3$ Then , since $0 \leq y,z \leq 1$ we have $$1 =y^2+z^2 \geq y^n+z^n =1$$ with equality if and only if $y^2=y^n, z^2=z^n$. >>Class 11>>Maths>>Trigonometric Functions>>Trigonometric Functions of Sum and Difference of Two angles>>Prove sinn + 1x sinn + 2 x + cos n Open in AppUpdated on 2022-09-05SolutionVerified by TopprTo prove- Proof Hence any question of Trigonometric Functions with-Was this answer helpful? 00More From ChapterLearn with Videos Practice more questions I'm studying convergent sequences at the moment. And I came across this question in the section of Stolz Theorem. I realised that $\{x_n\}$ is monotonously decreasing and has a lower bound of $0$, so $\{x_n\}$ must be convergent, and the limit is $0$ let $L=\sinL$, then $L=0$. So to prove the original statement, I just need to prove lim nXn^2 → 3, and in order to prove that, I just need to prove $\lim \frac{1}{x_n^2} - \frac{1}{{x_{n-1}}^2} \to \frac{1}{3}$ by Stolz Theorem but I have no clue what to do from there. PS $x_{n+1}$ is $x$ sub $n+1$, and $x_n$ is outside the square root. Thanks guys Question MediumOpen in AppSolutionVerified by TopprThe given equation is ...... i Let Therefore, from i, we get Since, both these values satisfy the given equation. Hence, the solutions of the given equation are .Video ExplanationWas this answer helpful? 00 Chapter 3 Class 11 Trigonometric Functions Serial order wise Ex Check sibling questions Ex Ex 1 Important Ex 2 Important Ex 3 Important Ex 4 Ex 5 i Important Ex 5 ii Ex 6 Important Ex 7 Ex 8 Important Ex 9 Important Ex 10 You are here Ex 11 Important Ex 12 Ex 13 Important Ex 14 Ex 15 Ex 16 Important Ex 17 Ex 18 Important Ex 19 Ex 20 Ex 21 Important Ex 22 Important Ex 23 Important Ex 24 Ex 25 Ex 10 - Chapter 3 Class 11 Trigonometric Functions Last updated at May 29, 2023 by Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class Transcript E 10 Prove that sin + 1 sin + 2 +cos + 1 cos + 2 =cos Taking We know that cos A B = cos A cos B + sin A sin B Hence A = n + 1x ,B = n + 2x Hence sin + 1 sin + 2 +cos + 1 cos + 2 = cos [ n + 1x n + 2x ] = cos [ nx + x nx 2x ] = cos [ nx nx x 2 x ] = cos 0 x = cos x = cos x = Hence , = Hence proved Chapter 3 Class 11 Trigonometric Functions Serial order wise Ex Ex 1 Important Ex 2 Important Ex 3 Important Ex 4 Ex 5 i Important Ex 5 ii Ex 6 Important Ex 7 Ex 8 Important Ex 9 Important Ex 10 You are here Ex 11 Important Ex 12 Ex 13 Important Ex 14 Ex 15 Ex 16 Important Ex 17 Ex 18 Important Ex 19 Ex 20 Ex 21 Important Ex 22 Important Ex 23 Important Ex 24 Ex 25 Davneet Singh has done his from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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