Check sibling questions

Ex 2.2, 8 - Chapter 2 Class 12 Inverse - tan-1 (cos x - sin x)

Ex 2.2, 8 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2


Transcript

Ex 2.2, 8 Write the function in the simplest form: tan−1 (cos⁡〖x − sin⁡x 〗/cos⁡〖x + sin⁡x 〗 ), 0 < x < π tan−1 (cos⁡〖x − sin⁡x 〗/cos⁡〖x + sin⁡x 〗 ) Dividing by cos x inside = tan−1 (((cos⁡𝑥 − sin⁡x)/cos⁡𝑥 )/((cos⁡𝑥 + sin⁡x)/cos⁡𝑥 )) = tan−1 (((cos x)/cos⁡〖x 〗 − (sin x)/cos⁡〖x 〗 )/((cos x)/cos⁡〖x 〗 + (sin x)/cos⁡〖x 〗 )) = tan−1 ((1 − tan⁡x)/(1 +〖 tan〗⁡x )) We write 𝐜𝐨𝐬⁡〖𝐱 − 𝐬𝐢𝐧⁡𝐱 〗/𝐜𝐨𝐬⁡〖𝐱 + 𝐬𝐢𝐧⁡𝐱 〗 in form of tan We know that tan (x – y) = 𝑡𝑎𝑛⁡〖𝑥 −〖 𝑡𝑎𝑛〗⁡〖𝑦 〗 〗/(1+ 𝑡𝑎𝑛⁡〖𝑥 𝑡𝑎𝑛⁡𝑦 〗 ) So, we divide whole equation by cos = tan−1 ((1 − tan⁡x)/(1 +〖 1 . tan〗⁡x )) = tan−1 ((𝒕𝒂𝒏⁡〖 𝝅/𝟒〗 − tan⁡𝑥)/(1 + 〖𝐭𝐚𝐧 〗⁡〖𝝅/𝟒 .〖 tan〗⁡𝑥 〗 )) = tan−1 ("tan " (𝜋/4−𝑥)) = 𝝅/𝟒 − x Using tan (x – y ) = 𝒕𝒂𝒏⁡〖𝒙 −〖 𝒕𝒂𝒏〗⁡〖𝒚 〗 〗/(𝟏+ 𝒕𝒂𝒏⁡〖𝒙 𝒕𝒂𝒏⁡𝒚 〗 ) Replace x by 𝜋/4 and y by x (As tan 𝜋/4 = 1 )

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.