Multiplyboth sides by n n. 1+sin(x) n n = kn 1 + sin ( x) n n = k n. Simplify the left side. Tap for more steps sin(x)+1 = kn sin ( x) + 1 = k n. Subtract 1 1 from both sides of the equation. sin(x) = kn−1 sin ( x) = k n - 1. Take the inverse sine of both sides of the equation to extract x x from inside the sine. Soif X n is the number of individuals alive in generation n, then X n+1 is the sum of X n -many independent, identically distributed random variables. Let's assume that X 0 = 1, p (0) > 0, and = k p (k) = E (X 1) 1. (a) If = 1 and 2 < , then there exist constants 0 < c 1 < c 2 < such that. c 1 /n < P ( X n 0 ) < c 2 /n. a) Prove the reduction formulaintegrate cos^n(x)dx = 1/n * cos^(n-1) * x sin x + (n-1)/n * integral cos^(n-2)x dx Thecorrect option is An sin n - 1 x cos n + 1 xExplanation for the correct option :Given, d sin n x cos n x d xFor differentiating this apply theorem for product d u × v d x = u d v d x + v d u d x⇒ d sin n x cos n x d x = n sin n - 1 x cos x cos n x + sin n x - sin n x n ⇒ d sin n x cos n x d x = n sin n - 1 x cos x cos n x - sin x sin n x Foreach of the following systems, determine whether the system is (a) linear, (b) (20 points) time-invariant, (c) causal, (dy memoryless, and (e) stable. (1) yln]xIn-11 sin [n] (2) y [n]-x [2n]+1 Time- Causal. sin (n+1)x sin (n+2)+cos (n+1)xcos (n+2)x = cosx - Brainly.in. GBO8s. 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.

sin n 1 x sin n 1 x