Verified answer

i) Next multiply by cos(3x), ==> sin(3x) + cos(3x) = 1

==> sin(3x) = 1 - cos(3x)

ii) Applying multiple angle identity,

2sin(3x/2)*cos(3x/2) = 2sin²(3x/2)

Rearranging and factorizing, 2sin(3x/2)[cos(3x/2) - sin(3x/2)] = 0

==> Either sin(3x/2) = 0 or cos(3x/2) - sin(3x/2) = 0

In the first case, when sin(3x/2) = 0, 3x/2 = 0 or in general it is nπ

==> x = 2nπ/3

In the second case, when cos(3x/2) - sin(3x/2) = 0

it is tan(3x/2) = 1

==> 3x/2 = π/4 ; ==> x = π/6

But at x = π/6, both left and right side each takes value = infinity.

Hence this is discarded.

So the only acceptable value is x = 2nπ/3

(tan o + a million) * (sec 0 - .5) = 0 answer from 0 to 360 Tan theta +a million = 0 and Sec theta -.5 = 0 Tan theta = -a million => a hundred thirty five, 315 : Tan function has a era of one hundred eighty stages. sec theta = .5 => cos theta = 2 => no longer conceivable root

(tan o + a million) * (sec 0 - .5) = 0 answer from 0 to 360 Tan theta +a million = 0 and Sec theta -.5 = 0 Tan theta = -a million => a hundred thirty five, 315 : Tan function has a era of one hundred eighty levels. sec theta = .5 => cos theta = 2 => no longer obtainable root

tan 3x +1 = sec 3x

(tan 3x +1)/(sec 3x) = (sec 3x)/(sec 3x)

(tan 3x)/(sec 3x) + (1)/(sec 3x) = 1

[(sin 3x)/(cos 3x)]/[(1)/(cos 3x)] + (1)/[(1)/(cos 3x)] = 1

[(sin 3x)(cos 3x)]/(cos 3x) + cos 3x = 1

sin 3x + cos 3x = 1

i tried but it's been too long since i did this..sorry bro