CBSE 12th Standard Maths Subject Inverse Trigonometric Functions HOT Questions 6 Mark Questions With Solution 2021
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CBSE 12th Standard Maths Subject Inverse Trigonometric Functions HOT Questions 6 Mark Questions With Solution 2021
12th Standard CBSE
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Reg.No. :
Maths
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Solve tan-1 2x + tan-13x = \(\frac { \pi }{ 4 } \)
(a)
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CBSE 12th Standard Maths Subject Inverse Trigonometric Functions HOT Questions 6 Mark Questions With Solution 2021 Answer Keys
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\(\text { We have } \tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}\)
\(\text { Or }\tan ^{-1}\left(\frac{2 x+3 x}{1-2 x \times 3 x}\right)=\frac{\pi}{4}\)
\(\text { i.e. }\tan ^{-1}\left(\frac{5 x}{1-6 x^{2}}\right)=\frac{\pi}{4}\)
\(\text { Therefore } \quad \frac{5 x}{1-6 x^{2}}=\tan \frac{\pi}{4}=1\)
\(\text { or } \quad 6 x^{2}+5 x-1=0 \text { i.e., }(6 x-1)(x+1)=0\)
\(\text { which gives } \ x=\frac{1}{6} \text { or } x=-1 .\)
Since x = – 1 does not satisfy the equation, as the L.H.S. of the equation becomes negative\(x=\frac{1}{6}\) is the only solution of the given equation
