Prove that 15C3+2×15C4+15C5=17C5
LHS=15C3+2×15C4+15C5=15C3+15C4+15C4+15C5=(15C4+15C3)+(15C5+15C4)=16C4+16C5[∵
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Prove the identity: $\dfrac{\sin \left(2 \alpha + \beta\right)}{\sin \alpha} - 2 \cos \left(\alpha + \beta\right) = \dfrac{\sin \beta...
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Prove the identity: \sec \left(\dfrac{\pi}{4} + \alpha\right) \sec \left(\dfrac{\pi}{4} - \alpha\right) = 2 \sec 2 \alpha LH...
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Two cyclists left the same point simultaneously and traveled in the same direction. The speed of the first was 15 km/h and that of th...