Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

How do u solve this trigonometry questions?

1. sin 5pi/ 9 cos pi/ 9 + cos 5pi/ 9 sin pi/ 9

2. (2 tan pi/ 8) / (1-tan^2 pi/ 8)

3. cos (1/6-2/7)

4. tan 2(1/6)

5. 2/(1-cos x) + 2/(1+cos x) = 4 csc^2 x

6. (sin x tan x) / (1-cos x) = 1 + sec x

7. 2sin(x+y) cos(x-y) = sin 2x + sin 2y

Relevance
• 1 month ago

sin(a)cos(b) + sin(b)cos(a) = sin(a + b)

sin(5pi/9 + pi/9) = sin(6pi/9) = sin(2pi/3) = sqrt(3)/2

2tan(t) / (1 - tan(t)^2) = tan(2t)

2tan(pi/8) / (1 - tan(pi/8)^2) = tan(2 * pi/8) = tan(pi/4) = 1

cos(1/6 - 2/7) =>

cos(7/42 - 12/42) =>

cos(-5/42)

tan2(1/6).  I have no idea what you're asking here

2/(1 - cos(x)) + 2/(1 + cos(x)) =>

(2 * (1 + cos(x)) + 2 * (1 - cos(x))) / (1 - cos(x)^2) =>

(2 + 2cos(x) + 2 - 2cos(x)) / sin(x)^2 =>

4 / sin(x)^2 =>

4 * csc(x)^2

(sin(x)tan(x)) / (1 - cos(x)) =>

(sin(x)^2 / cos(x)) * (1 + cos(x)) / (1 - cos(x)^2) =>

(1 + cos(x)) * sin(x)^2 / (cos(x) * sin(x)^2) =>

(1 + cos(x)) / cos(x) =>

1/cos(x) + cos(x)/cos(x) =>

1 + sec(x)

2sin(x + y)cos(x - y) =>

2 * (sin(x)cos(y) + sin(y)cos(x)) * (cos(x)cos(y) + sin(x)sin(y)) =>

2 * (sin(x)cos(x) * cos(y)^2 + sin(x)^2 * sin(y) * cos(y) + sin(y)cos(y) * cos(x)^2 + sin(x)cos(x) * sin(y)^2) =>

2 * (sin(x)cos(x) * (sin(y)^2 + cos(y)^2) + sin(y)cos(y) * (sin(x)^2 + cos(x)^2)) =>

2 * (sin(x)cos(x) * 1 + sin(y)cos(y) * 1) =>

2sin(x)cos(x) + 2sin(y)cos(y) =>

sin(2x) + sin(2y)