MHT CET · Maths · Inverse Trigonometric Functions
If , then
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4} \)
\( \tan ^{-1}\left(\frac{2 x+3 x}{1-6 x^2}\right)=\frac{\pi}{4} ; x>0 \)
\( \frac{5 x}{1-6 x^2}=1 \)
\( 5 x=1-6 x^2 \)
\( 6 x^2+5 x-1=0 \)
\( 6 x^2+6 x-x-1=0 \)
\( 6 x(x+1)-1(x+1)=0 \)
\( (6 x-1)(x+1)=0 \)
\( x \neq-1 ; x=\frac{1}{6}\)
\( \tan ^{-1}\left(\frac{2 x+3 x}{1-6 x^2}\right)=\frac{\pi}{4} ; x>0 \)
\( \frac{5 x}{1-6 x^2}=1 \)
\( 5 x=1-6 x^2 \)
\( 6 x^2+5 x-1=0 \)
\( 6 x^2+6 x-x-1=0 \)
\( 6 x(x+1)-1(x+1)=0 \)
\( (6 x-1)(x+1)=0 \)
\( x \neq-1 ; x=\frac{1}{6}\)
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