8 Solve the equation 2 sin 2x + cos 2x = 2, for 0° < x < 360°, using the substitution t = tan x. Give solutions correct to the nearest tenth of a degree where necessary.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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8 Solve the equation 2 sin 2x + cos 2x =
2, for 0° < x < 360°, using the substitution t = tan x. Give
solutions correct to the nearest tenth of a degree where necessary.
9 Suppose that a cos x =
1 + sin x, where 0° < x < 90°.
a
a Prove that
1
t, where t = tan x.
a + 1
b Hence find, correct to the nearest minute, the acute angle x that satisfies the equation
2 cos x
sin x
1.
Transcribed Image Text:8 Solve the equation 2 sin 2x + cos 2x = 2, for 0° < x < 360°, using the substitution t = tan x. Give solutions correct to the nearest tenth of a degree where necessary. 9 Suppose that a cos x = 1 + sin x, where 0° < x < 90°. a a Prove that 1 t, where t = tan x. a + 1 b Hence find, correct to the nearest minute, the acute angle x that satisfies the equation 2 cos x sin x 1.
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