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Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Subjective Questions

Q. 1. Find the value of : cos(2cos–1x + sin–1x) at x = 1/5, where 0 < cos–1 x < π and –π/2 < sin–1 x <  π/2.

Ans. Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solution. We have cos (2 cos–1 x + sin–1 x)
= cos (cos–1 x + cos–1 x + sin–1x)
= cos (cos–1 x + π/2) {Using cos–1 x + sin–1 x = π/2}
= – sin (cos–1 x)

Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 2. Find all the solution of 4 cos 2 x sin x - 2 sin2 x = 3 sinx

Ans. Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solution. Given eq. is,
4 cos2 x sin x – 2 sin2 x = 3 sin  x
⇒ 4 cos2 x sin x – 2 sin2 x – 3 sin x = 0
⇒ 4 (1 – sin2 x) sin x – 2 sin2 x – 3 sin x = 0
⇒ sin x [4 sin2 x + 2 sin x – 1] = 0
⇒ either sin x = 0 or 4 sin2 x + 2 sin x – 1 = 0
If sin x = 0 ⇒ x = nπ

⇒ If 4 sin2 x + 2 sin x – 1 = 0 ⇒  Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

where n is some integer


Q. 3. Prove that cos tan–1 sin cot–1Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solution.  To prove that cos tan–1 sin cot–1    Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

L.H.S. = cos [tan–1 (sin (cot–1x))]

Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
In each case,

Subjective Type Questions: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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