If one number is the multiple of another number, then the L.C.M. will be the smaller number (the number whose multiple the other number is).
Sum = n/2[2a + (n - 1)d] where a = first term, n = number of terms and d = common difference
(a) 30/2(2 x 5 + (30 - 1) x d) = 1455
10 + 29d = 1455 / 15
29d = 97 - 10
d = 87 / 29 = 3
(b) 7/2(2 x 9 + (7 - 1)d) = 0
18 + 6d = 0
6d = -18
d = -3
(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ =
= 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
Given:
The expression is
.
To find:
The shows the correct way to use the rule ""multiply by the reciprocal"" for the given expression.
Solution:
According to the rule "multiply by the reciprocal", if a,b,c,d are four number, then

We have,

It can be written as

Using the rule "multiply by the reciprocal", we get



Therefore, the correct option is D.
I thinks it’s A or C )) but it’s not b or d, I’m pretty sure. So imma go with A or c