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Naily [24]
3 years ago
7

What are all the exact solutions of 2sec^2x-tan^4x=-1 ?

Mathematics
1 answer:
Nataly_w [17]3 years ago
8 0
The first thing to do would be to simplify the equation first. Let's apply the trigonometric functions properties where 1 + tan²x = sec² x. So, we can substitute this to the equation so that it would purely be a function of tangents.

<span>2sec</span>²<span>x-tan</span>⁴<span>x=-1
2(1+tan</span>²x) - tan⁴x = 1
2 + 2 tan²x - tan⁴x + 1 = 0
tan⁴x - 2tan²x + 1 = 0
(tanx -1)² = 0
tanx - 1 = 0
tanx = 1
x = tan⁻¹ 1
x = 45°

So, the solution for the given trigonometric equation is 45° or π/4 radians.
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