Ex 3.3

Chapter 3 Class 11 Trigonometric Functions
Serial order wise

### Transcript

Ex 3.3, 23 Prove that tanβ‘4π₯ = (4 tanβ‘γπ₯ (1βtan2π₯)γ)/(1 β 6 tan2 π₯+tan4 π₯) Solving L.H.S. tan 4x We know that tan 2x = (2 π‘ππβ‘π₯)/(1 β π‘ππ2 π₯) Replacing x with 2x tan (2 Γ 2x) = (2 π‘ππβ‘2π₯)/(1 β π‘ππ2 2π₯) tan 4x = (2 π‘ππβ‘2π₯)/(1 β π‘ππ2 2π₯) = (π π­ππ§β‘ππ±)/(π β π­ππ§π ππ±) = 2((π πππβ‘π)/(π β ππππ π))/(1 β ((π πππβ‘π)/(π β ππππ π))^2 ) = (((4 tanβ‘π₯)/(1 β π‘ππ2 π₯)))/(1 β((2 tanβ‘π₯ )^2/(1 β π‘ππ2 π₯)^2 ) ) = (((4 tanβ‘π₯)/(1 β π‘ππ2 π₯)))/(1 β((4 γπ‘ππγ^2 π₯)/(1 β π‘ππ2 π₯)^2 ) ) = (((4 tanβ‘π₯)/(1 β π‘ππ2 π₯)))/((((1 β π‘ππ2 π₯)^2 β4 γπ‘ππγ^2 π₯)/(1 β π‘ππ2 π₯)^2 ) ) = (π πππβ‘π)/(π β π­ππ§πβ‘π ) Γ (π β π­ππ§πβ‘π )^π/((π β ππππ π)π βπ π­ππ§πβ‘π ) = (4 tanβ‘π₯)/1 Γ ((1 β tan2β‘γπ₯)γ)/((1 β π‘ππ2 π₯)2 β 4 tan2β‘π₯ ) = (π πππβ‘γπ (π β ππππ πγ))/((π βπ­ππ§πβ‘π )π β π πππβ‘ππ ) Using (a β b)2 = a2 + b2 β 2ab = (4 tanβ‘γπ₯ (1 β tan2β‘π₯)γ)/(( 12+(π‘ππ2 π₯)2 β 2 Γ 1 Γ π‘ππ2 π₯) β4 π‘ππ2 π₯) = (4 tanβ‘γπ₯ (1 β tan2β‘π₯)γ)/(1 + tanβ‘γ4 π₯ β 2 tan2β‘γπ₯ β4 tan2β‘π₯ γ γ ) = (π πππβ‘γπ (π β π­ππ§πβ‘γπ)γ γ)/(π + π­ππ§πβ‘γπ β π ππππ πγ ) = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.