Ex 2.2, 4 - Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at April 16, 2024 by Teachoo
Ex 2.2
Ex 2.2,1
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Chapter 2 Class 12 Inverse Trigonometric Functions
Serial order wise
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Transcript
Ex 2.2, 4 Write the function in the simplest form: tan−1 (√((1 −〖 cos〗x)/(1 +〖 cos〗x ))), x < π Lets first calculate values of 1 – cos x & 1 + cos x We know that cos 2x = 1 – 2sin2x Replacing x by 𝑥/2 cos (2𝑥/2) = 1 – 2 sin2 𝑥/2 cos (x) = 1 – 2 sin2 𝑥/2 2 sin2 𝑥/2 = 1 – cos x 1 – cos x = 2 sin2 𝑥/2 We know that cos 2x = 2 cos2x – 1 Replacing x by 𝑥/2 cos (2𝑥/2) = 2 cos2 𝑥/2 – 1 cos x = 2 cos2 𝑥/2 – 1 1 + cos x = 2 cos2 𝑥/2 Now, tan-1 (√((1 −〖 cos〗x)/(1 +〖 cos〗x ))) = tan−1 (√((𝟐 𝐬𝐢𝐧𝟐 𝐱/𝟐 )/(𝟐 𝐜𝐨𝐬𝟐 𝐱/𝟐))) = tan−1 (√((sin2 x/2 )/(cos2 x/2))) = tan−1 (√(tan2〖 𝑥/2〗 )) = tan−1 (tan〖 𝑥/2〗 ) = 𝒙/𝟐
