If 3sin−12x1+x2−4cos−11−x21+x2+2tan−12x1+x2=&

Sail E0 Webinar

Question

If

3 s i n^{- 1} \frac{2 x}{1 + x^{2}} - 4 c o s^{- 1} \frac{1 - x^{2}}{1 + x^{2}} + 2 t a n^{- 1} \frac{2 x}{1 + x^{2}} = \frac{π}{3}

then x=

Options:

A . √3

B . 1√3

C . 1

D . None of these

Answer: Option B
:
B

3 s i n^{- 1} \frac{2 x}{1 + x^{2}} - 4 c o s^{- 1} \frac{1 - x^{2}}{1 + x^{2}} + 2 t a n^{- 1} \frac{2 x}{1 + x^{2}} = \frac{π}{3}

Putting

x = t a n θ

3 s i n^{- 1} (\frac{2 t a n θ}{1 + t a n^{2} θ}) - 4 c o s^{- 1} (\frac{1 - t a n^{2} θ}{1 + t a n^{2} θ})

+ 2 t a n^{- 1} (\frac{2 t a n θ}{1 - t a n^{2} θ}) = \frac{π}{3}

\Rightarrow 3 s i n^{- 1} (s i n 2 θ) - 4 c o s^{- 1} (c o s 2 θ)

+ 2 t a n^{- 1} (t a n 2 θ) = \frac{π}{3}

\Rightarrow 3 (2 θ) - 4 (2 θ) + 2 (2 θ) = \frac{π}{3} \Rightarrow 6 θ - 8 θ + 4 θ = \frac{π}{3}

\Rightarrow θ = \frac{π}{6} \Rightarrow t a n^{- 1} x = \frac{π}{6} \Rightarrow x = t a n \frac{π}{6} = \frac{1}{\sqrt{3}}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The value of sin[2tan−1(13)]+cos[tan−1(2√2)]=....

Question 2. The value of cos−1(cos12)−sin−1(sin14) is....

Question 3. 3cos−1x−πx−π2=0 has : ....

Question 4. 12cos−1(1−x1+x)=....

Question 5. 4tan−115−tan−11239 is equal to....

Question 6. If cos−1x+cos−1y+cos−1z=3π, then xy+yz+zx= ....

Question 7. Sin(12cos−145)=....

Question 8. Cot−1[(cosα)12]−tan−1[(cosα)12]=x, then sinx=....

Question 9. If tan−1(x)+tan−1(y)+tan−1(z)=π, then 1xy+1yz+1zx=....

Question 10. If x=sin(2tan−12),y=sin(12tan−143) then....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0