Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Prove that $\cos^{-1}\left(\dfrac{4}{5}\right) + \cos^{-1}\left(\dfrac{12}{13}\right) = \cos^{-1}\left(\dfrac{33}{65}\right)$.
Step-by-Step Solution
$\cos A = 4/5, \sin A = 3/5$; $\cos B = 12/13, \sin B = 5/13$. [1.0 Mark]
$\cos(A+B) = (4/5)(12/13) - (3/5)(5/13) = 48/65 - 15/65 = 33/65$. [1.5 Marks]
$A+B = \cos^{-1}(33/65)$. Proved! [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding $\sin A$ and $\sin B$: 1.0 Mark
Applying $\cos(A+B)$ formula: 1.5 Marks
Concluding proof: 0.5 Mark
Correct Answer:
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