# Ex 2.2, 8 - Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)

Last updated at May 12, 2021 by Teachoo

Ex 2.2

Ex 2.2,1
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Chapter 2 Class 12 Inverse Trigonometric Functions

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Last updated at May 12, 2021 by Teachoo

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