Check sibling questions

Ex 3.3, 15 - Prove cot 4x (sin 5x + sin 3x) = cot x (sin 5x - cos x + cos y formula

Ex 3.3, 15 - Chapter 3 Class 11 Trigonometric Functions - Part 2

This video is only available for Teachoo black users


Transcript

Ex 3.3, 15 Prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x) Solving L.H.S. cot 4x ( sin 5x + sin 3x ) Using sin x + sin y = 2 sin (π‘₯ + 𝑦)/2 cos (π‘₯ βˆ’ 𝑦)/2 Putting x = 5x & y = 3x = cot 4x Γ— [ 2 sin ((5π‘₯ + 3π‘₯)/2) cos ((5π‘₯ βˆ’ 3π‘₯)/2) ] = cot 4x Γ— [ 2sin (8π‘₯/2) cos (2π‘₯/2)] = 2 cot 4x sin 4x cos x = 2 π‘π‘œπ‘ β‘4π‘₯/𝑠𝑖𝑛⁑4π‘₯ Γ— sin 4x Γ— cos x = 2 cos 4x cos x Solving R.H.S. cot x ( sin 5x – sin 3x ) Using sin x – sin y = 2 cos (π‘₯ + 𝑦)/2 sin (π‘₯ βˆ’ 𝑦)/2 Putting x = 5x & y = 3x = cot x ( 2 cos (5π‘₯ + 3π‘₯)/2 sin (5π‘₯ βˆ’ 3π‘₯)/2 ) = cot x ( 2 cos (8π‘₯/2) sin (2π‘₯/2)] = cot x ( 2 cos 4x sin x) = 2 cos 4x sin x cot x = 2 cos 4x sin x Γ— π‘π‘œπ‘ β‘π‘₯/sin⁑π‘₯ = 2 cos 4x cos x = L.H.S Hence L.H.S. = R.H.S. Hence Proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.