Question

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Answer 1

Answer:

6.

Tan(a+b) = root3

tan(a-b)= 1/root3

We know tan 60 = root 3 and tan 30 = 1/root3

So, a+b = 60, a-b = 30

Adding the two gives

a+a+b-b=60+30

2a=90

a = 45

a+b=60

45+b=60

b=15

7.

$let \: a \: be \: the \: first \: term \: and \: d \: the \: common \: difference \: of \: ap$

$a8 = 0 \\ a + (n - 1)d = 0 \\ a + (8 - 1)d = 0 \\ a + 7d = 0 \\ a = - 7d$

Equation (1)......

$\frac{a28}{a18} = \frac{a + 27d}{a + 17d} \\ \frac{a28}{a18} = \frac{ - 7d + 27d}{ - 7d + 17d}$

( From equation (1)......)

$\frac{a28}{a18} = \frac{20d}{10d} \\ \frac{a28}{a18} = \frac{2}{1} \\ a28 = 2 \times a18$

Hence, proved.

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Answer 2

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