How to do this ? Can anyone help me ?
1 answer:
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The dots in the patterns are illustrations of a sequence or progression
- The number of dots in step 10 is 84
- The number of dots in step n is (n -1)^2+ 3
From the pattern, we have:
- Step 0 = 3 dots
- Step 1 = 4 dots
- Step 2 = 7 dots
- Step 3 = 12 dots
So, we have the following pattern
When n = 10, we have:
T10 = 84
This means that, there will be 84 dots in step 10 and there will be (n -1)^2+ 3 dots in step n
Read more about sequence at:
(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