15 29. If tan A = – and tan B == 24...
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15 29. If tan A = – and tan B == 24 then cos(A – B) = ? RRB NTPC (Phase 1) 2016

11th - 12th Class
Maths
Solution
85
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29. (1) Now, In figure by applying Pythgoras theorem [ begin{aligned} A B^{2}+B C^{2} &=A C^{2} 15^{2}+8^{2} &=A C^{2} Rightarrow A C=17 end{aligned} ] Similarly, ( P R=25 ) By using Trigonometric ratio ( cos A^{circ}=frac{8}{17}, cos B^{circ}=frac{24}{25}, sin A^{circ}=frac{15}{17} ) ( sin B^{circ}=frac{7}{25} ) Now, ( cos (A-B)=cos A^{circ} cos B^{circ}+sin A^{circ} sin B^{circ} ) [by sum and difference formulae] ( =frac{8}{17} times frac{24}{25}+frac{15}{17} times frac{7}{25}=frac{297}{425} )
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