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Maru [420]
2 years ago
15

Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that​

Mathematics
1 answer:
igor_vitrenko [27]2 years ago
8 0

Take L.H.S sin2A+sin2B/sin2A-sin2B

= sin2A+sin2B/sin2A-sin2B

Put

[sinC+sinD = 2sin(C+D)/2cos(C-D)/2]

[sinC-sinD = 2cos(C+D)/2.sin(C-D)/2]

= 2 sin(2A+2B)/2 cos(2A-2B)/2 / 2 cos(2A+2B) sin(2A-2B)

= sin(A+B).cos(A-B)/cos(A+B).sin(A-B)

= sin(A+B)/cos(A+B) . cos(A-B)/sin(A-B)

= tan(A+B).cot(A-B)

= tan(A+B).1/tan(A-B)

= tan(A+B)/tan(A-B)

∴ Hence we proved sin2A+sin2B/sin2A-sin2B=tan(A+B)/tan(A-B)

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         20% of $5 is $1,   so $5 + $1 = $6

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Each of the remaining articles is sold at a price that's 50% of the 260 he sold.

         He sold those for $6,  so he would now sell the last 40 for $3

               From the remaining 40 articles, he makes 40 * $3, or $120

The shopkeeper made $1560 + $120 = $1680,  which is $180 more than he bought them for ($1500)

Therefore, he made a profit percentage of $180 / $1500,  (the amount of profit over the amount spent).

He made a profit percentage, compared to the cost price, of 12%.

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