Last updated at March 11, 2017 by Teachoo

Transcript

Misc 10 Prove cot-1 ((√(1 + sin〖x 〗 ) + √(1 − sinx ))/(√(1 +〖 sin〗x ) − √(1 − sinx ))) = 𝑥/2 , x ∈ (0, 𝜋/4) First, finding √(1+sin𝑥 ) & √(1−sin𝑥 ) cot-1 ((√(1 + sinx ) + √(1 − sinx ))/(√(1 + sinx ) − √(1 −〖 sin〗x ))) = cot-1 (("(sin " 𝑥/2 " + cos " 𝑥/2 )+" cos " 𝑥/2 "− sin " 𝑥/2)/("sin " 𝑥/2 " + cos " 𝑥/2 " − (cos " 𝑥/2 "− sin " 𝑥/2))) = cot-1 (("sin " 𝑥/2 −" sin " 𝑥/2 +" cos " 𝑥/2 + " cos " 𝑥/2)/("cos " 𝑥/2 "− cos " 𝑥/2 +" sin " 𝑥/2 + "sin " 𝑥/2)) = cot-1 ((0 +〖 2cos〗〖 𝑥/2〗)/(0 + 2sin〖 𝑥/2〗 )) = cot-1 ((2 cos x/2 )/〖2 sin〗〖 x/2 〗 ) = cot-1 (cot x/2) = x/2 = R.H.S.

Chapter 2 Class 12 Inverse Trigonometric Functions

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.