Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Prove that $\tan^{-1}\left(\dfrac{1}{5}\right) + \tan^{-1}\left(\dfrac{1}{7}\right) + \tan^{-1}\left(\dfrac{1}{3}\right) + \tan^{-1}\left(\dfrac{1}{8}\right) = \dfrac{\pi}{4}$.
Step-by-Step Solution
Pair 1 $= \tan^{-1}(6/17)$, Pair 2 $= \tan^{-1}(11/23)$. [1.5 Marks]
Total $= \tan^{-1}\left(\dfrac{138+187}{391-66}\right) = \tan^{-1}(325/325) = \tan^{-1}(1) = \pi/4$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating pair 1 and pair 2 sums: 1.5 Marks
Combining sums to get $\tan^{-1}(1) = \pi/4$: 1.5 Marks
Correct Answer:
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