PLS FRIENDS HELP ME WITH THESE QUESTIONS

1.FIND THE PRINCIPAL VALUE OF SEC^-1 (-2) + SIN^-1 (SIN 2PIE /3)

2.SOLVE TAN^-1 (1+X) + TAN^-1 (X-1)= TAN^-1 6/17

3. PROVE THAT 2TAN^-1 1/5 + SEC^-1 5 SQUARE ROOT 2/7 + 2TAN^-1 1/8= PIE/4

Question

PLS FRIENDS HELP ME WITH THESE QUESTIONS
1 FIND THE PRINCIPAL VALUE OF SEC-1 (-2) +
SIN-1 (SIN 2PIE /3)
2 SOLVE TAN-1 (1+X) + TAN-1 (X-1)=
TAN-1 6/17
3 PROVE THAT 2TAN-1 1/5 + SEC-1 5 SQUARE
ROOT 2/7 + 2TAN-1 1/8= PIE/4

ramandeep.singh · Accepted Answer

Q2 $\tan^{-1} (1 + x) + \tan^{-1} (x - 1) = \tan^{-1} (\frac{6}{17}) \Rightarrow \tan^{-1} (\frac{1 + x + x - 1}{1 - (1 + x) (x - 1)}) = \tan^{-1} (\frac{6}{17}) ∴ \frac{2 x}{2 - x^{2}} = \frac{6}{17} \Rightarrow 3 x^{2} + 17 x - 6 = 0 \Rightarrow 3 x^{2} + 18 x - x - 6 = 0 \Rightarrow (3 x - 1) (x + 6) = 0 ∴ 3 x - 1 = 0 o r x + 6 = 0 \Rightarrow x = \frac{1}{3} o r x = - 6$ Q3 L H S $2 \tan^{-1} (\frac{1}{5}) + \sec^{- 1} (\frac{5 \sqrt{2}}{7}) + 2 \tan^{-1} (\frac{1}{8}) = 2 [\tan^{-1} (\frac{1}{5}) + \tan^{-1} (\frac{1}{8})] + \sec^{- 1} (\frac{5 \sqrt{2}}{7}) = 2 \tan^{- 1} (\frac{\frac{1}{5} + \frac{1}{8}}{1 - \frac{1}{5} \times \frac{1}{8}}) + \tan^{- 1} \sqrt{(\frac{5 \sqrt{2}}{7})^{2} - 1} = 2 \tan^{- 1} \frac{1}{3} + \tan^{- 1} \frac{1}{7} = \tan^{- 1} (\frac{2 \times \frac{1}{3}}{1 - ({\frac{1}{3})}^{2}}) + \tan^{- 1} \frac{1}{7} = \tan^{- 1} \frac{3}{4} + \tan^{- 1} \frac{1}{7} = \tan^{- 1} (\frac{\frac{3}{4} + \frac{1}{7}}{1 - \frac{3}{4} \times \frac{1}{7}}) = \tan^{- 1} 1 = \frac{π}{4}$ Due to paucity of time it would not be possible for us to provide the answers to all your queries We are providing solutions to some of your good queries Try solving the rest of the questions yourself and if you face any difficulty then do get back to us

PLS FRIENDS HELP ME WITH THESE QUESTIONS 1.FIND THE PRINCIPAL VALUE OF SEC-1 (-2) + SIN-1 (SIN 2PIE /3) 2.SOLVE TAN-1 (1+X) + TAN-1 (X-1)= TAN-1 6/17 3. PROVE THAT 2TAN-1 1/5 + SEC-1 5 SQUARE ROOT 2/7 + 2TAN-1 1/8= PIE/4

PLS FRIENDS HELP ME WITH THESE QUESTIONS

1.FIND THE PRINCIPAL VALUE OF SEC^-1 (-2) + SIN^-1 (SIN 2PIE /3)

2.SOLVE TAN^-1 (1+X) + TAN^-1 (X-1)= TAN^-1 6/17

3. PROVE THAT 2TAN^-1 1/5 + SEC^-1 5 SQUARE ROOT 2/7 + 2TAN^-1 1/8= PIE/4