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vodomira [7]
1 year ago
15

Which shows all the exact solutions of 2sec^2 (x)-tan^4 (x)=-1? Give your answer in radians.

Mathematics
1 answer:
shutvik [7]1 year ago
4 0

Answer:

a. 1/3pi+kpi and 2/3pi+kpi

Step-by-step explanation:

2Sec²x

=2+2tan²x-(tan²x)²=-1

Let tan²x=u

-u²+2u+2=-1

-u²+2u+3=0

u²-2u-3=0

(u+1)(u-3)=0

u=-1,u=3

(tan x)²=-1(No solution)

(tan x)²=3

>>tan x=±sqrt(3)

I) tan x=sqrt(3)

>>tan(pi/3)=sqrt 3

Tan(pi+A) =tanA

Tan(pi+pi/3)=tan(pi/3)

>>tan(4/3pi)=sqrt(3)

>>x=4/3pi and 1/3pi

General solution: 1/3pi+kpi

ii) tan x=-sqrt(3)

x=2/3pi(At 2nd quadrant)

x=5/3pi(at 4th quadrant)

General solution: 2/3pi+kpi

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Question 12 1 pts If the population of a country is reported in the year 1990 as 471.56 million and in the year 2000 as 492.53 m
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__

The closest answer choice is 526.39 million.

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<em>Comment on the answer choice</em>

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