Question

In ΔABC, BC = 5, AC = 4 and cos(A-B)=7/8. Find the value of 96 cosC.

Answer 1

Step-by-step explanation:

Given In ∆ABC, <ABC = 90°

AB = 6 units , BC = 8 units

By Phythogarian theorem:

i) AC² = AB²+BC²

= 6²+8²

= 36+64

= 100

=> AC = √100

=> AC = 10 units.

ii)sinA = BC/AC = 8/10

cosC = BC/AC = 8/10

cosA = AB/AC = 6/10

sinC = AB/AC = 6/10

Now ,

sinAcosC+cosAsinC

= \frac{8}{10}\times\frac{8}{10}+\frac{6}{10}\times\frac{6}{10}

10

8

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×

10

8

+

10

6

×

10

6

= \frac{64}{100}+\frac{36}{100}

100

64

+

100

36

= \frac{64+36}{100}

100

64+36

= \frac{100}{100}

100

100

= 11

Therefore,

sinAcosC+cosAsinC =1