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Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Fill in the Blanks

Q. 1. Let a, b, c be positive real numbers. Let

Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Then  tan θ = _________

Ans. 0

Solution. Let a + b + c = u, then

Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

[Using tan–1 (– x) = – tan–1 x] = π
∴ tan θ = tan π = 0


Q. 2. The numerical value of tan Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE equal to _________

Ans. -7/17

Solution. 

Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 3. The greater of the two angles A = 2 tan -1 (2 √2 - 1) and B = 3 sin -1 (1/3) + sin -1 (3/5) is _________ .

Ans. A

Solution. We have

Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
⇒  A > 2π /3    ... (1)

Also B = 3 sin–1 (1/3) + sin–1(3/5)

Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Inverse Trigonometric Functions | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒ B < 2π /3 ....(2)
From (1) and (2) we conclude A > B.

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